CMPINF-2100 Final Project¶
Spotify Song Popularity – Regression Analysis¶
This notebook follows the project structure:
- Introduction
- EDA
- Clustering
- Models: Fitting and Interpretation
- Models: Predictions
- Models: Performance and Validation
We use the TidyTuesday Spotify dataset (2020-01-21) and treat track_popularity
as a continuous response variable (regression).
Import Modules¶
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.preprocessing import StandardScaler, OneHotEncoder
from sklearn.compose import ColumnTransformer
from sklearn.cluster import KMeans
from sklearn.model_selection import train_test_split, KFold, cross_val_score
from sklearn.pipeline import Pipeline
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score, mean_squared_error
import statsmodels.formula.api as smf
Read data¶
songs_url = 'https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2020/2020-01-21/spotify_songs.csv'
spotify = pd.read_csv(songs_url)
1. Introduction¶
We analyze the Spotify songs dataset from the TidyTuesday project (2020-01-21)
as a regression problem. The response is track_popularity (0–100).
Goal:
Understand and predict how audio characteristics (e.g., danceability, energy, valence),
song characteristics (duration_ms, tempo), and contextual information (playlist_genre,
playlist_subgenre, release_year) relate to track popularity as a continuous variable ( regression problem).
High-level summary of findings (to be completed after analysis): Which inputs/features seem to influence the response/outcome the most? What supported your conclusion? Was it only through predictive models?
- Artist popularity, artist hit rate, playlist popularity are significant predictors of popular tracks
- There are some subgenres like pop teen that significantly increase the odd of track being popular.
- There are audio characteristics, that when interacted with the significant predictors mentioned above, which increase the odd of track being successful, such as danceability, energy, and instrmentalness.
- This will be seen below from the multiple regression that have been tested. It will also show through the EDA section.
Was clustering consistent with any conclusions from the predictive models?
- Clustering supported the notion that popular tracks are driven by artist related and playlist related features.
iWhat skills did you learn from going through this project?
I have learned many valuable skills including:
- Data Analysis
- Programming
- Data Vizualization
- Modelling
This project have made me greatly progress in the aquistiion and mastery of data science.
EDA¶
Basic Information¶
spotify.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 32833 entries, 0 to 32832 Data columns (total 23 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 track_id 32833 non-null object 1 track_name 32828 non-null object 2 track_artist 32828 non-null object 3 track_popularity 32833 non-null int64 4 track_album_id 32833 non-null object 5 track_album_name 32828 non-null object 6 track_album_release_date 32833 non-null object 7 playlist_name 32833 non-null object 8 playlist_id 32833 non-null object 9 playlist_genre 32833 non-null object 10 playlist_subgenre 32833 non-null object 11 danceability 32833 non-null float64 12 energy 32833 non-null float64 13 key 32833 non-null int64 14 loudness 32833 non-null float64 15 mode 32833 non-null int64 16 speechiness 32833 non-null float64 17 acousticness 32833 non-null float64 18 instrumentalness 32833 non-null float64 19 liveness 32833 non-null float64 20 valence 32833 non-null float64 21 tempo 32833 non-null float64 22 duration_ms 32833 non-null int64 dtypes: float64(9), int64(4), object(10) memory usage: 5.8+ MB
spotify.dtypes
track_id object track_name object track_artist object track_popularity int64 track_album_id object track_album_name object track_album_release_date object playlist_name object playlist_id object playlist_genre object playlist_subgenre object danceability float64 energy float64 key int64 loudness float64 mode int64 speechiness float64 acousticness float64 instrumentalness float64 liveness float64 valence float64 tempo float64 duration_ms int64 dtype: object
spotify.isna().sum().sort_values(ascending=False)
track_artist 5 track_album_name 5 track_name 5 track_id 0 key 0 tempo 0 valence 0 liveness 0 instrumentalness 0 acousticness 0 speechiness 0 mode 0 loudness 0 danceability 0 energy 0 playlist_subgenre 0 playlist_genre 0 playlist_id 0 playlist_name 0 track_album_release_date 0 track_album_id 0 track_popularity 0 duration_ms 0 dtype: int64
spotify.nunique().sort_values(ascending=False)
track_id 28356 track_name 23449 track_album_id 22545 duration_ms 19785 track_album_name 19743 tempo 17684 track_artist 10692 loudness 10222 instrumentalness 4729 track_album_release_date 4530 acousticness 3731 liveness 1624 valence 1362 speechiness 1270 energy 952 danceability 822 playlist_id 471 playlist_name 449 track_popularity 101 playlist_subgenre 24 key 12 playlist_genre 6 mode 2 dtype: int64
spotify["track_album_release_date"] = pd.to_datetime(
spotify["track_album_release_date"], errors="coerce"
)
spotify["release_year"] = spotify["track_album_release_date"].dt.year
spotify["release_month"] = spotify["track_album_release_date"].dt.month
b. Visualization¶
continuous_vars = [
"danceability", "energy", "loudness", "speechiness",
"acousticness", "instrumentalness", "liveness", "valence",
"tempo", "duration_ms"
]
categorical_vars = ["playlist_genre", "playlist_subgenre", "mode","key"]
vars_to_plot = ["track_popularity", "danceability", "energy", "valence", "duration_ms"]
- Counts of categorical variables
sns.catplot( data = spotify , kind = 'count', x = 'playlist_genre',aspect=1.5)
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
sns.catplot( data = spotify , kind = 'count', x = 'playlist_subgenre', aspect = 6)
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
plt.figure(figsize=(10, 4))
sns.countplot(data=spotify, x="playlist_subgenre", order=spotify["playlist_subgenre"].value_counts().index[:10])
plt.xticks(rotation=45)
plt.title("Counts of top 10 playlist_subgenre")
plt.tight_layout()
plt.show()
- Distributions of continuous variables
spotify_lm = spotify.reset_index().rename(columns={'index':'row_id'}).melt(id_vars=categorical_vars, value_vars=continuous_vars)
sns.displot( data = spotify_lm , x = 'value', col = 'variable', kind = 'hist', aspect = 2, col_wrap=3, facet_kws={'sharex': False, 'sharey': False}, common_bins=False, kde=True)
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
plt.figure(figsize=(14, 8))
for i, var in enumerate(vars_to_plot, start=1):
plt.subplot(2, 3, i)
sns.histplot(data=spotify, x=var, bins=30, kde=True)
plt.title(var)
plt.tight_layout()
plt.show()
- Relationships between continuous variables
corr_cols = ["track_popularity"] + continuous_vars
corr = spotify[corr_cols].corr()
plt.figure(figsize=(10, 8))
sns.heatmap(corr, cmap="coolwarm", center=0,annot=True,vmin=-1,vmax=1)
plt.title("Correlation heatmap: popularity and continuous features")
plt.tight_layout()
plt.show()
This corr plot summarizes the relationship between the continious variables. Track popularity is not strongly correlated with any 'one' audio characetristic.
sns.pairplot(spotify[continuous_vars + ["track_popularity"]],diag_kws={'common_norm':False})
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
sample_df = spotify.sample(5000, random_state=0)
plt.figure(figsize=(15, 4))
for i, var in enumerate(["danceability", "energy", "valence"], start=1):
plt.subplot(1, 3, i)
sns.scatterplot(data=sample_df, x=var, y="track_popularity", alpha=0.3)
plt.title("Popularity vs " + var)
plt.tight_layout()
plt.show()
- Summaries of the continuous variables grouped by categorical variables
sns.catplot(data = spotify, x="playlist_genre", y="track_popularity", kind="box", aspect=1.5)
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
--- 2.7 Summaries grouped by categorical variables ---
group_summary = (
spotify
.groupby("playlist_genre")[["track_popularity"] + continuous_vars]
.mean()
.sort_values("track_popularity", ascending=False)
)
group_summary
| track_popularity | danceability | energy | loudness | speechiness | acousticness | instrumentalness | liveness | valence | tempo | duration_ms | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| playlist_genre | |||||||||||
| pop | 47.744870 | 0.639302 | 0.701028 | -6.315328 | 0.073991 | 0.170794 | 0.059876 | 0.176833 | 0.503521 | 120.743178 | 217768.104231 |
| latin | 47.026576 | 0.713287 | 0.708312 | -6.264455 | 0.102653 | 0.210920 | 0.044447 | 0.180626 | 0.605510 | 118.622354 | 216863.446945 |
| rap | 43.215454 | 0.718353 | 0.650708 | -7.042269 | 0.197506 | 0.192479 | 0.075997 | 0.191654 | 0.505090 | 120.654908 | 214163.889140 |
| rock | 41.728338 | 0.520548 | 0.732813 | -7.588895 | 0.057696 | 0.145189 | 0.062417 | 0.203135 | 0.537352 | 124.988786 | 248576.500303 |
| r&b | 41.223532 | 0.670179 | 0.590934 | -7.864848 | 0.116792 | 0.259904 | 0.028920 | 0.175268 | 0.531231 | 114.222156 | 237599.489781 |
| edm | 34.833526 | 0.655041 | 0.802476 | -5.427445 | 0.086695 | 0.081504 | 0.218578 | 0.211859 | 0.400656 | 125.768024 | 222540.858349 |
spotify\
.groupby(["playlist_genre"])[["track_popularity"]+continuous_vars]\
.mean().reset_index().sort_values("track_popularity", ascending=False)
| playlist_genre | track_popularity | danceability | energy | loudness | speechiness | acousticness | instrumentalness | liveness | valence | tempo | duration_ms | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | pop | 47.744870 | 0.639302 | 0.701028 | -6.315328 | 0.073991 | 0.170794 | 0.059876 | 0.176833 | 0.503521 | 120.743178 | 217768.104231 |
| 1 | latin | 47.026576 | 0.713287 | 0.708312 | -6.264455 | 0.102653 | 0.210920 | 0.044447 | 0.180626 | 0.605510 | 118.622354 | 216863.446945 |
| 4 | rap | 43.215454 | 0.718353 | 0.650708 | -7.042269 | 0.197506 | 0.192479 | 0.075997 | 0.191654 | 0.505090 | 120.654908 | 214163.889140 |
| 5 | rock | 41.728338 | 0.520548 | 0.732813 | -7.588895 | 0.057696 | 0.145189 | 0.062417 | 0.203135 | 0.537352 | 124.988786 | 248576.500303 |
| 3 | r&b | 41.223532 | 0.670179 | 0.590934 | -7.864848 | 0.116792 | 0.259904 | 0.028920 | 0.175268 | 0.531231 | 114.222156 | 237599.489781 |
| 0 | edm | 34.833526 | 0.655041 | 0.802476 | -5.427445 | 0.086695 | 0.081504 | 0.218578 | 0.211859 | 0.400656 | 125.768024 | 222540.858349 |
spotify\
.groupby(["playlist_subgenre"])[["track_popularity"]+continuous_vars]\
.mean().reset_index().sort_values("track_popularity", ascending=False)
| playlist_subgenre | track_popularity | danceability | energy | loudness | speechiness | acousticness | instrumentalness | liveness | valence | tempo | duration_ms | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 17 | post-teen pop | 56.825509 | 0.635626 | 0.716008 | -5.540277 | 0.082358 | 0.153024 | 0.009367 | 0.180314 | 0.555087 | 123.850051 | 208598.733392 |
| 15 | permanent wave | 54.000905 | 0.530724 | 0.709683 | -7.580004 | 0.050507 | 0.144509 | 0.087302 | 0.189590 | 0.545103 | 124.876413 | 244210.825339 |
| 9 | hip pop | 53.844745 | 0.675424 | 0.621870 | -6.871198 | 0.122393 | 0.255173 | 0.031629 | 0.172780 | 0.514428 | 116.026076 | 211897.167994 |
| 8 | hip hop | 53.773071 | 0.719628 | 0.565940 | -8.243336 | 0.189124 | 0.308059 | 0.218851 | 0.173616 | 0.509257 | 118.260575 | 181696.042360 |
| 19 | reggaeton | 52.869336 | 0.760954 | 0.746515 | -5.336615 | 0.123065 | 0.201285 | 0.003761 | 0.182066 | 0.678986 | 119.256106 | 218115.869336 |
| 3 | dance pop | 52.079353 | 0.655752 | 0.742189 | -5.768586 | 0.075837 | 0.144161 | 0.048890 | 0.176795 | 0.505211 | 120.106639 | 207832.938367 |
| 12 | latin pop | 51.099842 | 0.686111 | 0.689050 | -6.186886 | 0.090443 | 0.247439 | 0.014786 | 0.188604 | 0.607369 | 119.638224 | 216682.389065 |
| 23 | urban contemporary | 50.523843 | 0.651922 | 0.572769 | -7.625293 | 0.130267 | 0.298932 | 0.023077 | 0.172841 | 0.470657 | 118.260871 | 228450.264057 |
| 21 | trap | 50.308288 | 0.715405 | 0.655576 | -6.528663 | 0.144863 | 0.216218 | 0.067978 | 0.166972 | 0.437307 | 130.034411 | 200910.660728 |
| 16 | pop edm | 45.686223 | 0.647744 | 0.742543 | -5.453845 | 0.085093 | 0.136459 | 0.047935 | 0.196825 | 0.464772 | 123.169141 | 205710.918260 |
| 11 | latin hip hop | 43.451087 | 0.723135 | 0.726298 | -6.195614 | 0.123441 | 0.152912 | 0.043954 | 0.176899 | 0.618276 | 119.127287 | 225658.317029 |
| 22 | tropical | 43.327640 | 0.692133 | 0.675914 | -7.112600 | 0.072849 | 0.256820 | 0.104120 | 0.176538 | 0.533140 | 116.510839 | 204810.373447 |
| 5 | electropop | 42.725142 | 0.638609 | 0.723269 | -6.567401 | 0.069747 | 0.134555 | 0.100840 | 0.182373 | 0.512342 | 122.357326 | 235876.772017 |
| 10 | indie poptimism | 42.475478 | 0.629596 | 0.640230 | -7.050846 | 0.070483 | 0.233985 | 0.068015 | 0.169848 | 0.459962 | 117.780169 | 216423.044856 |
| 2 | classic rock | 40.809414 | 0.545396 | 0.699240 | -8.287437 | 0.052463 | 0.191351 | 0.050040 | 0.191167 | 0.609958 | 123.612147 | 256666.654321 |
| 0 | album rock | 38.322066 | 0.525020 | 0.664189 | -8.888486 | 0.051450 | 0.205905 | 0.075451 | 0.222909 | 0.520844 | 122.464300 | 255363.044131 |
| 20 | southern hip hop | 36.445970 | 0.714681 | 0.680922 | -6.908566 | 0.201511 | 0.117409 | 0.022481 | 0.209483 | 0.554183 | 119.118353 | 247029.002985 |
| 7 | hard rock | 35.841077 | 0.488084 | 0.828541 | -6.053844 | 0.072091 | 0.061864 | 0.045356 | 0.209477 | 0.480058 | 128.084324 | 239897.417508 |
| 4 | electro house | 35.510258 | 0.701628 | 0.800044 | -5.842447 | 0.093483 | 0.092875 | 0.321228 | 0.192536 | 0.428701 | 124.976406 | 216682.578425 |
| 6 | gangster rap | 35.139232 | 0.724025 | 0.688549 | -6.561617 | 0.247118 | 0.152902 | 0.015051 | 0.209384 | 0.504932 | 116.285976 | 217581.821674 |
| 13 | neo soul | 32.687233 | 0.645015 | 0.541685 | -8.332789 | 0.122204 | 0.314412 | 0.041362 | 0.177927 | 0.510043 | 110.101762 | 239197.748931 |
| 1 | big room | 32.282753 | 0.619551 | 0.860316 | -4.703041 | 0.093293 | 0.042411 | 0.238905 | 0.251372 | 0.324091 | 128.872881 | 203852.392206 |
| 14 | new jack swing | 28.032657 | 0.723365 | 0.650324 | -8.587335 | 0.086053 | 0.137996 | 0.015188 | 0.177191 | 0.655586 | 113.167402 | 275128.552515 |
| 18 | progressive electro house | 26.867883 | 0.645908 | 0.816206 | -5.541605 | 0.077971 | 0.051983 | 0.262385 | 0.214263 | 0.374506 | 126.538718 | 254006.402985 |
Teen pop is the most popular subgenre playlist.
spotify\
.groupby(["playlist_subgenre"])["track_popularity"]\
.mean().reset_index().sort_values("track_popularity", ascending=False)
| playlist_subgenre | track_popularity | |
|---|---|---|
| 17 | post-teen pop | 56.825509 |
| 15 | permanent wave | 54.000905 |
| 9 | hip pop | 53.844745 |
| 8 | hip hop | 53.773071 |
| 19 | reggaeton | 52.869336 |
| 3 | dance pop | 52.079353 |
| 12 | latin pop | 51.099842 |
| 23 | urban contemporary | 50.523843 |
| 21 | trap | 50.308288 |
| 16 | pop edm | 45.686223 |
| 11 | latin hip hop | 43.451087 |
| 22 | tropical | 43.327640 |
| 5 | electropop | 42.725142 |
| 10 | indie poptimism | 42.475478 |
| 2 | classic rock | 40.809414 |
| 0 | album rock | 38.322066 |
| 20 | southern hip hop | 36.445970 |
| 7 | hard rock | 35.841077 |
| 4 | electro house | 35.510258 |
| 6 | gangster rap | 35.139232 |
| 13 | neo soul | 32.687233 |
| 1 | big room | 32.282753 |
| 14 | new jack swing | 28.032657 |
| 18 | progressive electro house | 26.867883 |
Duplicated data¶
In this section, only the code will be done to remove duplicated rows from the dataset. This will ensure that the analysis and results are more reliable.
spotify = spotify.loc[~spotify.track_id.duplicated(), :]
Clustering: Revisited¶
In this iteration of the clustering exercise, we will apply hierarchial clustering.
cluster_vars = [
"danceability", "energy", "loudness", "speechiness",
"acousticness", "instrumentalness", "liveness", "valence",
"tempo", "duration_ms"
]
spotify_cluster = spotify.dropna(subset=cluster_vars + ["track_popularity"]).copy()
X_cluster = spotify_cluster[cluster_vars].values
X_scaled = StandardScaler().fit_transform(X_cluster)
inertias = []
ks = list(range(1,20))
for k in ks:
km = KMeans(n_clusters=k, n_init=10, random_state=0)
km.fit(X_scaled)
inertias.append(km.inertia_)
plt.figure(figsize=(6, 4))
plt.plot(ks, inertias, marker="o")
plt.xlabel("Number of clusters (k)")
plt.ylabel("Inertia (within-cluster SSE)")
plt.title("Elbow plot for k-means clustering")
plt.tight_layout()
plt.show()
We will try hierarchial clustering.
from scipy.cluster import hierarchy
hclust_ward = hierarchy.ward(X_scaled)
fig = plt.figure(figsize=(12, 7))
dn = hierarchy.dendrogram(hclust_ward, no_labels=True)
plt.show()
It seems that we have 6 distinct clusters.
spotify['k'] = pd.Series(hierarchy.cut_tree(hclust_ward, n_clusters=4).ravel(),index = spotify.index).astype('category')
sns.catplot(data = spotify , x="k", y="track_popularity", kind="box", aspect=1)
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
spotify.groupby('k')[continuous_vars + ['track_popularity']].mean()
| danceability | energy | loudness | speechiness | acousticness | instrumentalness | liveness | valence | tempo | duration_ms | track_popularity | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| k | |||||||||||
| 0 | 0.652164 | 0.736680 | -6.260000 | 0.076657 | 0.123858 | 0.021978 | 0.207172 | 0.542251 | 121.422971 | 226445.501476 | 39.903129 |
| 1 | 0.709523 | 0.675679 | -6.743498 | 0.294719 | 0.154332 | 0.006747 | 0.175967 | 0.529467 | 121.869349 | 219106.025151 | 39.818913 |
| 2 | 0.657353 | 0.718471 | -7.829748 | 0.077385 | 0.162057 | 0.712202 | 0.159662 | 0.400815 | 122.983098 | 231470.241071 | 31.884615 |
| 3 | 0.578474 | 0.457930 | -9.547663 | 0.083113 | 0.575174 | 0.025900 | 0.137563 | 0.386748 | 114.525539 | 232882.608113 | 42.522751 |
sns.catplot(data = spotify , x= 'k' , kind = 'count', aspect=1)
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
sns.catplot(data = spotify , x= 'k' , kind = 'count', aspect=1, hue='playlist_genre')
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
sns.catplot(data = spotify , y= 'k' , kind = 'count', aspect=1, hue='release_year')
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
spotify.groupby('k')[continuous_vars + ['track_popularity','playlist_genre']].count()
| danceability | energy | loudness | speechiness | acousticness | instrumentalness | liveness | valence | tempo | duration_ms | track_popularity | playlist_genre | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| k | ||||||||||||
| 0 | 18633 | 18633 | 18633 | 18633 | 18633 | 18633 | 18633 | 18633 | 18633 | 18633 | 18633 | 18633 |
| 1 | 3976 | 3976 | 3976 | 3976 | 3976 | 3976 | 3976 | 3976 | 3976 | 3976 | 3976 | 3976 |
| 2 | 2912 | 2912 | 2912 | 2912 | 2912 | 2912 | 2912 | 2912 | 2912 | 2912 | 2912 | 2912 |
| 3 | 2835 | 2835 | 2835 | 2835 | 2835 | 2835 | 2835 | 2835 | 2835 | 2835 | 2835 | 2835 |
pd.crosstab(spotify['k'], spotify['playlist_genre'])
| playlist_genre | edm | latin | pop | r&b | rap | rock |
|---|---|---|---|---|---|---|
| k | ||||||
| 0 | 3087 | 3090 | 3873 | 2714 | 2446 | 3423 |
| 1 | 295 | 459 | 305 | 738 | 2130 | 49 |
| 2 | 1393 | 234 | 371 | 122 | 500 | 292 |
| 3 | 102 | 354 | 583 | 930 | 325 | 541 |
spotify.groupby('k')[continuous_vars + ['track_popularity']].mean()
| danceability | energy | loudness | speechiness | acousticness | instrumentalness | liveness | valence | tempo | duration_ms | track_popularity | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| k | |||||||||||
| 0 | 0.652164 | 0.736680 | -6.260000 | 0.076657 | 0.123858 | 0.021978 | 0.207172 | 0.542251 | 121.422971 | 226445.501476 | 39.903129 |
| 1 | 0.709523 | 0.675679 | -6.743498 | 0.294719 | 0.154332 | 0.006747 | 0.175967 | 0.529467 | 121.869349 | 219106.025151 | 39.818913 |
| 2 | 0.657353 | 0.718471 | -7.829748 | 0.077385 | 0.162057 | 0.712202 | 0.159662 | 0.400815 | 122.983098 | 231470.241071 | 31.884615 |
| 3 | 0.578474 | 0.457930 | -9.547663 | 0.083113 | 0.575174 | 0.025900 | 0.137563 | 0.386748 | 114.525539 | 232882.608113 | 42.522751 |
Modeling¶
There are some variables that we want to create specifically for modelling.
def my_coefplot(mod, figsize_use=(10, 4)):
fig, ax = plt.subplots(figsize=figsize_use)
ax.errorbar( y=mod.params.index,
x=mod.params,
xerr = 2 * mod.bse,
fmt='o', color='k', ecolor='k', elinewidth=2, ms=10)
ax.axvline(x=0, linestyle='--', linewidth=3.5, color='grey')
ax.set_xlabel('coefficient value')
plt.show()
spotify.info()
<class 'pandas.core.frame.DataFrame'> Index: 28356 entries, 0 to 32832 Data columns (total 26 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 track_id 28356 non-null object 1 track_name 28352 non-null object 2 track_artist 28352 non-null object 3 track_popularity 28356 non-null int64 4 track_album_id 28356 non-null object 5 track_album_name 28352 non-null object 6 track_album_release_date 26675 non-null datetime64[ns] 7 playlist_name 28356 non-null object 8 playlist_id 28356 non-null object 9 playlist_genre 28356 non-null object 10 playlist_subgenre 28356 non-null object 11 danceability 28356 non-null float64 12 energy 28356 non-null float64 13 key 28356 non-null int64 14 loudness 28356 non-null float64 15 mode 28356 non-null int64 16 speechiness 28356 non-null float64 17 acousticness 28356 non-null float64 18 instrumentalness 28356 non-null float64 19 liveness 28356 non-null float64 20 valence 28356 non-null float64 21 tempo 28356 non-null float64 22 duration_ms 28356 non-null int64 23 release_year 26675 non-null float64 24 release_month 26675 non-null float64 25 k 28356 non-null category dtypes: category(1), datetime64[ns](1), float64(11), int64(4), object(9) memory usage: 5.7+ MB
spotify_model = spotify.copy()
artist_vars = spotify.groupby(['track_artist']).agg(
artist_avg_popularity=('track_popularity','mean'),
artist_n_tracks=('track_popularity','count'),
artist_n_genres=('playlist_genre','nunique'),
artist_n_playlists=('playlist_id','nunique'),
artist_n_subgenres=('playlist_subgenre','nunique'),
artist_hit_rate=('track_popularity', lambda x: np.where(x > 70,1,0).mean()),
artist_energy_mean=('energy','mean'),
artist_danceability_mean=('danceability','mean'),
artist_valence_mean=('valence','mean'),
artist_tempo_mean=('tempo','mean'),
artist_acousticness_mean=('acousticness','mean'),
artist_speechiness_mean=('speechiness','mean'),
artist_instrumentalness_mean=('instrumentalness','mean'),
artist_liveness_mean=('liveness','mean')
).reset_index().sort_values(by='artist_n_playlists', ascending=False)
playlist_vars = spotify.groupby(['playlist_id']).agg(
playlist_avg_popularity=('track_popularity','mean'),
playlist_n_tracks=('track_popularity','count'),
playlist_n_genres=('playlist_genre','nunique'),
playlist_n_subgenres=('playlist_subgenre','nunique')
).reset_index().sort_values(by='playlist_n_tracks', ascending=False)
spotify_model = spotify_model.merge(artist_vars, on='track_artist', how='inner')
spotify_model = spotify_model.merge(playlist_vars, on='playlist_id', how='inner')
def fit_ols(formula, data):
model = smf.ols(formula=formula, data=data).fit()
print(model.summary())
return model
def viz_fitted_vs_actual(fitted, actual, title):
df_viz = pd.DataFrame({
'Fitted Values': fitted,
'Actual Values': actual
})
plt.figure(figsize=(6,6))
sns.scatterplot(data=df_viz, x='Actual Values', y='Fitted Values', alpha=0.3)
sns.lineplot(data=df_viz, x='Actual Values', y='Actual Values', color='red')
plt.title(title)
plt.show()
Are the variables Gaussian ?
spotify_lm = spotify_model.reset_index().rename(columns={'index':'row_id'}).melt(id_vars=categorical_vars, value_vars=continuous_vars+artist_vars.columns.tolist()[1:])
sns.displot( data = spotify_lm , x = 'value', col = 'variable', kind = 'hist', aspect = 2, col_wrap=3, facet_kws={'sharex': False, 'sharey': False}, common_bins=False, kde=True)
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
As is shown by the graph above, the new variable avg_artist_popularity, seems to follow gaussian distribution. The remainin artist related variables will remain as categorical variables. Hence, it is not necessary that are Gaussian like.
However, we will drop artist_n_playlist becasue this kind of information will be already captured essentially in artist_n_genres. Plus, it is easier to work with artist_n_genres since there are only 5 unique values. For the same reason, we will also drop artist_n_subgenre.
We will go ahead and start fitting models.
But first we will first apply natural to some variables and then standardize the values of continious variables.
spotify_model.isna().sum().sort_values(ascending=False)
release_year 1681 release_month 1681 track_album_release_date 1681 track_id 0 artist_n_subgenres 0 k 0 artist_avg_popularity 0 artist_n_tracks 0 artist_n_genres 0 artist_n_playlists 0 artist_hit_rate 0 tempo 0 artist_energy_mean 0 artist_danceability_mean 0 artist_valence_mean 0 artist_tempo_mean 0 artist_acousticness_mean 0 artist_speechiness_mean 0 artist_instrumentalness_mean 0 duration_ms 0 valence 0 track_name 0 playlist_subgenre 0 track_artist 0 track_popularity 0 track_album_id 0 track_album_name 0 playlist_name 0 playlist_id 0 playlist_genre 0 danceability 0 liveness 0 energy 0 key 0 loudness 0 mode 0 speechiness 0 acousticness 0 instrumentalness 0 artist_liveness_mean 0 dtype: int64
cat_var = ['playlist_subgenre', 'mode','artist_n_genres']
cont_var = ['danceability', 'energy','speechiness',
'acousticness', 'instrumentalness', 'liveness', 'valence',
'tempo', 'duration_ms', 'artist_avg_popularity',
'artist_n_tracks',
'artist_hit_rate',
'artist_energy_mean',
'artist_danceability_mean',
'artist_valence_mean',
'artist_tempo_mean',
'artist_acousticness_mean',
'artist_speechiness_mean',
'artist_instrumentalness_mean',
'artist_liveness_mean','playlist_avg_popularity']
cont_features = (
"danceability + energy + speechiness + acousticness + instrumentalness + liveness + valence + \
tempo + duration_ms + artist_avg_popularity + artist_hit_rate + \
artist_n_tracks + artist_energy_mean + artist_danceability_mean + artist_valence_mean + artist_tempo_mean + \
artist_acousticness_mean + artist_speechiness_mean + artist_instrumentalness_mean + artist_liveness_mean+ playlist_avg_popularity"
)
cat_features = "playlist_subgenre + mode + artist_n_genres + key"
'Artist_n_tracks' has more than needed unique values. Therefore, we will group values together to make the modelling work easier to interpret as a categorical variable.
#spotify_model['artist_n_tracks'] = pd.to_numeric(spotify_copy['artist_n_tracks'])
#spotify_model['artist_n_tracks'] = np.where(spotify_copy['artist_n_tracks']<20,'Low',
# np.where(spotify_copy['artist_n_tracks']<40,'Medium','High'))
Natural log of all continious variables.
spotify_model[cont_var] = np.log1p(spotify_model[cont_var])
Now we visualize all continious variables to ensure Gaussian like behaviour.
spotify_lm = spotify_model.reset_index().rename(columns={'index':'row_id'}).melt(id_vars=cat_var, value_vars=cont_var)
sns.displot( data = spotify_lm , x = 'value', col = 'variable', kind = 'hist', aspect = 2, col_wrap=3, facet_kws={'sharex': False, 'sharey': False},kde=True)
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
spotify_model[cat_var] = spotify_model[cat_var].astype('category')
Standardization
x_scaled = pd.DataFrame(StandardScaler().fit_transform(spotify_model[cont_var]), columns=cont_var)
# Fix the typo
spotify_model[cont_var] = pd.DataFrame(
StandardScaler().fit_transform(spotify_model[cont_var]),
columns=cont_var,
index=spotify_model.index # Add this line to preserve the index
)
Intercept-only model
f_1 = "track_popularity ~ 1"
m_1 = fit_ols(f_1, spotify_model)
OLS Regression Results
==============================================================================
Dep. Variable: track_popularity R-squared: 0.000
Model: OLS Adj. R-squared: 0.000
Method: Least Squares F-statistic: nan
Date: Tue, 09 Dec 2025 Prob (F-statistic): nan
Time: 17:26:10 Log-Likelihood: -1.2998e+05
No. Observations: 28352 AIC: 2.600e+05
Df Residuals: 28351 BIC: 2.600e+05
Df Model: 0
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 39.3353 0.141 279.471 0.000 39.059 39.611
==============================================================================
Omnibus: 6116.318 Durbin-Watson: 1.122
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1389.583
Skew: -0.232 Prob(JB): 1.80e-302
Kurtosis: 2.019 Cond. No. 1.00
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
my_coefplot(m_1, figsize_use=(8,6))
How many coefficients were estimated?
m_1.params.size
1
How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?
m_1.params[m_1.pvalues < 0.05].size
1
WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?
m_1.params[m_1.pvalues < 0.05]
Intercept 39.33532 dtype: float64
Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values
m1.params[m1.pvalues < 0.05].sort_values(key=abs,ascending=False)
Intercept 39.33532 dtype: float64
Training Performance
print(f'R squared: {m1.rsquared}, RMSE: {m1.mse_resid**0.5}')
R squared: 0.0, RMSE: 23.69944331918895
Observed vs Predicted figure
viz_fitted_vs_actual(m1.fittedvalues, spotify_model['track_popularity'], 'Intercept only Model')
Categorical inputs with additive features
f_2 = "track_popularity ~ +" + cat_features
m_2 = fit_ols(f_2, spotify_model)
OLS Regression Results
==============================================================================
Dep. Variable: track_popularity R-squared: 0.158
Model: OLS Adj. R-squared: 0.158
Method: Least Squares F-statistic: 183.9
Date: Tue, 09 Dec 2025 Prob (F-statistic): 0.00
Time: 17:26:14 Log-Likelihood: -1.2753e+05
No. Observations: 28352 AIC: 2.551e+05
Df Residuals: 28322 BIC: 2.554e+05
Df Model: 29
Covariance Type: nonrobust
==================================================================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------------------------------------------
Intercept 35.3501 0.744 47.503 0.000 33.892 36.809
playlist_subgenre[T.big room] -8.9385 0.960 -9.315 0.000 -10.819 -7.058
playlist_subgenre[T.classic rock] 0.1173 0.941 0.125 0.901 -1.728 1.962
playlist_subgenre[T.dance pop] 12.2696 0.912 13.461 0.000 10.483 14.056
playlist_subgenre[T.electro house] -3.2797 0.891 -3.679 0.000 -5.027 -1.533
playlist_subgenre[T.electropop] -0.7196 0.919 -0.783 0.434 -2.521 1.082
playlist_subgenre[T.gangster rap] -4.7416 0.906 -5.236 0.000 -6.517 -2.967
playlist_subgenre[T.hard rock] -3.3554 0.923 -3.636 0.000 -5.164 -1.547
playlist_subgenre[T.hip hop] 15.8711 0.909 17.466 0.000 14.090 17.652
playlist_subgenre[T.hip pop] 6.4456 1.025 6.290 0.000 4.437 8.454
playlist_subgenre[T.indie poptimism] 2.4823 0.874 2.842 0.004 0.770 4.194
playlist_subgenre[T.latin hip hop] -5.2220 0.928 -5.629 0.000 -7.040 -3.404
playlist_subgenre[T.latin pop] 9.4415 0.942 10.020 0.000 7.595 11.288
playlist_subgenre[T.neo soul] -6.7874 0.885 -7.671 0.000 -8.522 -5.053
playlist_subgenre[T.new jack swing] -11.6645 0.958 -12.175 0.000 -13.542 -9.787
playlist_subgenre[T.permanent wave] 13.9897 0.973 14.380 0.000 12.083 15.897
playlist_subgenre[T.pop edm] -2.9426 0.979 -3.007 0.003 -4.861 -1.024
playlist_subgenre[T.post-teen pop] 14.5635 0.963 15.121 0.000 12.676 16.451
playlist_subgenre[T.progressive electro house] -14.0040 0.887 -15.794 0.000 -15.742 -12.266
playlist_subgenre[T.reggaeton] 7.0243 1.074 6.541 0.000 4.919 9.129
playlist_subgenre[T.southern hip hop] -2.8892 0.870 -3.320 0.001 -4.595 -1.183
playlist_subgenre[T.trap] 10.8537 0.924 11.744 0.000 9.042 12.665
playlist_subgenre[T.tropical] 4.0332 0.932 4.329 0.000 2.207 5.859
playlist_subgenre[T.urban contemporary] 7.9415 0.928 8.560 0.000 6.123 9.760
mode[T.1] 0.0280 0.268 0.104 0.917 -0.497 0.553
artist_n_genres[T.2] 5.3978 0.327 16.497 0.000 4.757 6.039
artist_n_genres[T.3] 8.9565 0.449 19.947 0.000 8.076 9.837
artist_n_genres[T.4] 11.4734 0.596 19.265 0.000 10.306 12.641
artist_n_genres[T.5] 5.3364 1.064 5.013 0.000 3.250 7.423
key -0.0050 0.036 -0.137 0.891 -0.076 0.066
==============================================================================
Omnibus: 1833.362 Durbin-Watson: 1.296
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1266.200
Skew: -0.408 Prob(JB): 1.12e-275
Kurtosis: 2.363 Cond. No. 171.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
my_coefplot(m_2, figsize_use=(8,12))
How many coefficients were estimated?
m_2.params.size
30
How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?
print(m_2.params[m_2.pvalues < 0.05].size)
26
WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?
m_2.params[m_2.pvalues < 0.05]
Intercept 35.350127 playlist_subgenre[T.big room] -8.938483 playlist_subgenre[T.dance pop] 12.269645 playlist_subgenre[T.electro house] -3.279704 playlist_subgenre[T.gangster rap] -4.741553 playlist_subgenre[T.hard rock] -3.355361 playlist_subgenre[T.hip hop] 15.871143 playlist_subgenre[T.hip pop] 6.445567 playlist_subgenre[T.indie poptimism] 2.482334 playlist_subgenre[T.latin hip hop] -5.222045 playlist_subgenre[T.latin pop] 9.441476 playlist_subgenre[T.neo soul] -6.787420 playlist_subgenre[T.new jack swing] -11.664472 playlist_subgenre[T.permanent wave] 13.989716 playlist_subgenre[T.pop edm] -2.942566 playlist_subgenre[T.post-teen pop] 14.563470 playlist_subgenre[T.progressive electro house] -14.004006 playlist_subgenre[T.reggaeton] 7.024311 playlist_subgenre[T.southern hip hop] -2.889238 playlist_subgenre[T.trap] 10.853732 playlist_subgenre[T.tropical] 4.033236 playlist_subgenre[T.urban contemporary] 7.941489 artist_n_genres[T.2] 5.397848 artist_n_genres[T.3] 8.956454 artist_n_genres[T.4] 11.473385 artist_n_genres[T.5] 5.336372 dtype: float64
Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?
print(m_2.params[m_2.pvalues < 0.05].sort_values(key=abs,ascending=False)[1:3])
playlist_subgenre[T.hip hop] 15.871143 playlist_subgenre[T.post-teen pop] 14.563470 dtype: float64
Show the predicted vs observed figure for the training set, and the R-squared and RMSE on the training set.
def viz_fitted_vs_actual(fitted, actual, title):
df_viz = pd.DataFrame({
'Fitted Values': fitted,
'Actual Values': actual
})
plt.figure(figsize=(6,6))
sns.scatterplot(data=df_viz, x='Actual Values', y='Fitted Values', alpha=0.3)
sns.lineplot(data=df_viz, x='Actual Values', y='Actual Values', color='red')
plt.title(title)
plt.show()
viz_fitted_vs_actual(m_2.fittedvalues, spotify_model['track_popularity'],'Categorical only Model')
Training performance
print(f'R squared: {m_cat.rsquared}, RMSE: {m_cat.mse_resid**0.5}')
R squared: 0.15849282400371167, RMSE: 21.75150385497045
Categorical only model barely does better than the intercept only model as indicated by RMSE of 21 vs 23.
Continuous inputs with linear additive features¶
f_3 = "track_popularity ~ " + cont_features
m_3 = fit_ols(f_3, spotify_model)
OLS Regression Results
==============================================================================
Dep. Variable: track_popularity R-squared: 0.528
Model: OLS Adj. R-squared: 0.527
Method: Least Squares F-statistic: 1507.
Date: Wed, 10 Dec 2025 Prob (F-statistic): 0.00
Time: 03:46:45 Log-Likelihood: -1.1934e+05
No. Observations: 28352 AIC: 2.387e+05
Df Residuals: 28330 BIC: 2.389e+05
Df Model: 21
Covariance Type: nonrobust
================================================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------------------------
Intercept 39.3353 0.097 406.485 0.000 39.146 39.525
danceability 0.6810 0.183 3.725 0.000 0.323 1.039
energy -1.1725 0.199 -5.883 0.000 -1.563 -0.782
speechiness -0.2949 0.170 -1.734 0.083 -0.628 0.038
acousticness 0.1728 0.182 0.951 0.341 -0.183 0.529
instrumentalness -1.0286 0.191 -5.380 0.000 -1.403 -0.654
liveness -0.2052 0.130 -1.577 0.115 -0.460 0.050
valence 0.4998 0.175 2.857 0.004 0.157 0.843
tempo 0.1822 0.136 1.344 0.179 -0.084 0.448
duration_ms 0.0120 0.101 0.118 0.906 -0.186 0.210
artist_avg_popularity 9.9201 0.116 85.453 0.000 9.693 10.148
artist_hit_rate 3.7516 0.109 34.514 0.000 3.539 3.965
artist_n_tracks -0.8198 0.105 -7.803 0.000 -1.026 -0.614
artist_energy_mean 0.8152 0.212 3.844 0.000 0.399 1.231
artist_danceability_mean -0.5015 0.188 -2.672 0.008 -0.869 -0.134
artist_valence_mean -0.1989 0.177 -1.126 0.260 -0.545 0.147
artist_tempo_mean -0.0279 0.137 -0.204 0.839 -0.297 0.241
artist_acousticness_mean -0.2629 0.195 -1.346 0.178 -0.646 0.120
artist_speechiness_mean 0.2223 0.174 1.279 0.201 -0.118 0.563
artist_instrumentalness_mean 1.1505 0.195 5.913 0.000 0.769 1.532
artist_liveness_mean 0.0987 0.133 0.744 0.457 -0.161 0.359
playlist_avg_popularity 8.0040 0.118 67.683 0.000 7.772 8.236
==============================================================================
Omnibus: 1996.522 Durbin-Watson: 1.559
Prob(Omnibus): 0.000 Jarque-Bera (JB): 2555.827
Skew: -0.650 Prob(JB): 0.00
Kurtosis: 3.688 Cond. No. 6.40
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
my_coefplot(m_3)
i. How many coefficients were estimated?
10 Coefficients were estimated.
ii. How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds? Nearly all coefficients are statsitically significant except for mode.
iii. WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features? iv. Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?
How many coefficients were estimated?
m_3.params.size
22
How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?
m_3.params[m_3.pvalues < 0.05].size
12
WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?
m_3.params[m_3.pvalues < 0.05]
Intercept 39.335320 danceability 0.681033 energy -1.172547 instrumentalness -1.028642 valence 0.499804 artist_avg_popularity 9.920143 artist_hit_rate 3.751601 artist_n_tracks -0.819824 artist_energy_mean 0.815204 artist_danceability_mean -0.501500 artist_instrumentalness_mean 1.150451 playlist_avg_popularity 8.003964 dtype: float64
Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?
m_3.params[m_3.pvalues < 0.05].sort_values(key=abs,ascending=False)[1:3]
artist_avg_popularity 13.358650 artist_hit_rate 5.209513 dtype: float64
For each model show the predicted vs observed figure for the training set, and the R-squared and RMSE on the training set.
print(f'R squared: {m_3.rsquared}, RMSE: {m_3.mse_resid**0.5}')
R squared: 0.5276510268815217, RMSE: 16.294105968324935
viz_fitted_vs_actual(m_3.fittedvalues, spotify_model['track_popularity'], 'Continuous only Model')
All inputs (continuous + categorical) additive¶
f_4 = (
"track_popularity ~ " + cont_features + " + " + cat_features
)
m_4 = fit_ols(f_4, spotify_model)
OLS Regression Results
==============================================================================
Dep. Variable: track_popularity R-squared: 0.533
Model: OLS Adj. R-squared: 0.533
Method: Least Squares F-statistic: 688.5
Date: Wed, 10 Dec 2025 Prob (F-statistic): 0.00
Time: 03:49:48 Log-Likelihood: -1.1917e+05
No. Observations: 28352 AIC: 2.384e+05
Df Residuals: 28304 BIC: 2.388e+05
Df Model: 47
Covariance Type: nonrobust
==================================================================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------------------------------------------
Intercept 42.1861 0.599 70.481 0.000 41.013 43.359
playlist_subgenre[T.big room] -3.0296 0.785 -3.860 0.000 -4.568 -1.491
playlist_subgenre[T.classic rock] -2.9838 0.706 -4.226 0.000 -4.368 -1.600
playlist_subgenre[T.dance pop] 1.7435 0.717 2.430 0.015 0.337 3.150
playlist_subgenre[T.electro house] -2.4618 0.736 -3.345 0.001 -3.904 -1.019
playlist_subgenre[T.electropop] -0.5550 0.707 -0.785 0.433 -1.941 0.831
playlist_subgenre[T.gangster rap] -4.3557 0.759 -5.739 0.000 -5.843 -2.868
playlist_subgenre[T.hard rock] -4.1508 0.711 -5.836 0.000 -5.545 -2.757
playlist_subgenre[T.hip hop] 0.3768 0.760 0.496 0.620 -1.112 1.866
playlist_subgenre[T.hip pop] -0.6393 0.800 -0.799 0.424 -2.208 0.929
playlist_subgenre[T.indie poptimism] -1.4229 0.679 -2.096 0.036 -2.754 -0.092
playlist_subgenre[T.latin hip hop] 0.7046 0.737 0.956 0.339 -0.740 2.149
playlist_subgenre[T.latin pop] -1.5018 0.734 -2.046 0.041 -2.940 -0.063
playlist_subgenre[T.neo soul] -1.1221 0.694 -1.618 0.106 -2.482 0.237
playlist_subgenre[T.new jack swing] -4.7197 0.748 -6.306 0.000 -6.187 -3.253
playlist_subgenre[T.permanent wave] 1.0189 0.740 1.377 0.169 -0.432 2.470
playlist_subgenre[T.pop edm] -3.3656 0.765 -4.399 0.000 -4.865 -1.866
playlist_subgenre[T.post-teen pop] 2.5951 0.746 3.477 0.001 1.132 4.058
playlist_subgenre[T.progressive electro house] -0.9300 0.728 -1.277 0.202 -2.358 0.498
playlist_subgenre[T.reggaeton] -2.1048 0.842 -2.501 0.012 -3.754 -0.455
playlist_subgenre[T.southern hip hop] -3.6225 0.708 -5.114 0.000 -5.011 -2.234
playlist_subgenre[T.trap] -1.8376 0.749 -2.452 0.014 -3.306 -0.369
playlist_subgenre[T.tropical] -2.3484 0.737 -3.186 0.001 -3.793 -0.904
playlist_subgenre[T.urban contemporary] -0.2052 0.725 -0.283 0.777 -1.625 1.215
danceability 0.6975 0.182 3.834 0.000 0.341 1.054
energy -1.0954 0.199 -5.516 0.000 -1.485 -0.706
speechiness -0.2468 0.169 -1.459 0.145 -0.578 0.085
acousticness 0.1571 0.181 0.869 0.385 -0.197 0.511
instrumentalness -0.9825 0.190 -5.158 0.000 -1.356 -0.609
liveness -0.1880 0.129 -1.453 0.146 -0.442 0.066
valence 0.4461 0.174 2.559 0.011 0.104 0.788
tempo 0.1757 0.135 1.302 0.193 -0.089 0.440
duration_ms 0.0989 0.105 0.939 0.348 -0.108 0.305
artist_avg_popularity 10.0953 0.117 86.537 0.000 9.867 10.324
artist_hit_rate 3.7024 0.115 32.276 0.000 3.478 3.927
artist_n_tracks -0.2432 0.134 -1.813 0.070 -0.506 0.020
artist_energy_mean 0.8602 0.217 3.967 0.000 0.435 1.285
artist_danceability_mean -0.3533 0.199 -1.774 0.076 -0.744 0.037
artist_valence_mean -0.3473 0.182 -1.906 0.057 -0.705 0.010
artist_tempo_mean -0.0310 0.137 -0.226 0.822 -0.300 0.238
artist_acousticness_mean -0.3456 0.197 -1.756 0.079 -0.731 0.040
artist_speechiness_mean 0.4145 0.185 2.240 0.025 0.052 0.777
artist_instrumentalness_mean 0.9694 0.198 4.905 0.000 0.582 1.357
artist_liveness_mean 0.1215 0.132 0.918 0.359 -0.138 0.381
playlist_avg_popularity 7.5881 0.130 58.155 0.000 7.332 7.844
mode 0.1186 0.200 0.593 0.553 -0.273 0.510
artist_n_genres -0.9449 0.143 -6.618 0.000 -1.225 -0.665
key 0.0200 0.027 0.737 0.461 -0.033 0.073
==============================================================================
Omnibus: 1978.851 Durbin-Watson: 1.576
Prob(Omnibus): 0.000 Jarque-Bera (JB): 2524.834
Skew: -0.648 Prob(JB): 0.00
Kurtosis: 3.677 Cond. No. 187.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
my_coefplot(m_all, figsize_use=(10,12))
How many coefficients were estimated?
m_4.params.size
48
How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?
m_4.params[m_4.pvalues < 0.05].size
27
WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?
m_4.params[m_4.pvalues < 0.05]
Intercept 42.186147 playlist_subgenre[T.big room] -3.029620 playlist_subgenre[T.classic rock] -2.983779 playlist_subgenre[T.dance pop] 1.743533 playlist_subgenre[T.electro house] -2.461842 playlist_subgenre[T.gangster rap] -4.355652 playlist_subgenre[T.hard rock] -4.150836 playlist_subgenre[T.indie poptimism] -1.422858 playlist_subgenre[T.latin pop] -1.501753 playlist_subgenre[T.new jack swing] -4.719727 playlist_subgenre[T.pop edm] -3.365604 playlist_subgenre[T.post-teen pop] 2.595075 playlist_subgenre[T.reggaeton] -2.104822 playlist_subgenre[T.southern hip hop] -3.622466 playlist_subgenre[T.trap] -1.837599 playlist_subgenre[T.tropical] -2.348388 danceability 0.697492 energy -1.095441 instrumentalness -0.982516 valence 0.446091 artist_avg_popularity 10.095314 artist_hit_rate 3.702357 artist_energy_mean 0.860172 artist_speechiness_mean 0.414505 artist_instrumentalness_mean 0.969382 playlist_avg_popularity 7.588078 artist_n_genres -0.944934 dtype: float64
Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?
m_4.params[m_4.pvalues < 0.05].sort_values(key=abs,ascending=False)[1:3]
artist_avg_popularity 10.095314 playlist_avg_popularity 7.588078 dtype: float64
Training Performance
print(f'R squared: {m_4.rsquared}, RMSE: {m_4.mse_resid**0.5}')
R squared: 0.5334176551680413, RMSE: 16.20177433293829
The performance is certianly better than average as shown by the higher r squared and lower rmse. However, it is only bit better than continuous terms only.
Continuous inputs with linear main effect and pair-wise interactions.¶
f_5 = "track_popularity ~ (danceability + energy + speechiness + acousticness + instrumentalness + liveness + valence + tempo + duration_ms \
+ artist_avg_popularity + artist_hit_rate + artist_n_tracks + playlist_avg_popularity )**2"
m_5 = fit_ols(f_5, spotify_model)
OLS Regression Results
==============================================================================
Dep. Variable: track_popularity R-squared: 0.582
Model: OLS Adj. R-squared: 0.581
Method: Least Squares F-statistic: 432.2
Date: Wed, 10 Dec 2025 Prob (F-statistic): 0.00
Time: 03:50:58 Log-Likelihood: -1.1761e+05
No. Observations: 28352 AIC: 2.354e+05
Df Residuals: 28260 BIC: 2.362e+05
Df Model: 91
Covariance Type: nonrobust
=================================================================================================================
coef std err t P>|t| [0.025 0.975]
-----------------------------------------------------------------------------------------------------------------
Intercept 35.5263 0.185 192.019 0.000 35.164 35.889
danceability 0.0442 0.110 0.401 0.689 -0.172 0.261
energy -0.4793 0.126 -3.792 0.000 -0.727 -0.232
speechiness -0.0622 0.105 -0.593 0.553 -0.268 0.143
acousticness -0.0199 0.127 -0.157 0.876 -0.269 0.229
instrumentalness 0.0408 0.141 0.289 0.773 -0.236 0.318
liveness -0.0995 0.100 -0.997 0.319 -0.295 0.096
valence 0.2222 0.107 2.084 0.037 0.013 0.431
tempo 0.1154 0.114 1.016 0.310 -0.107 0.338
duration_ms 0.2685 0.107 2.507 0.012 0.059 0.478
artist_avg_popularity 17.1344 0.245 69.937 0.000 16.654 17.615
artist_hit_rate -3.2118 0.328 -9.780 0.000 -3.856 -2.568
artist_n_tracks 0.2544 0.110 2.310 0.021 0.039 0.470
playlist_avg_popularity 8.9896 0.123 73.021 0.000 8.748 9.231
danceability:energy -0.1635 0.124 -1.321 0.186 -0.406 0.079
danceability:speechiness 0.1115 0.109 1.022 0.307 -0.102 0.325
danceability:acousticness 0.2622 0.122 2.146 0.032 0.023 0.502
danceability:instrumentalness 0.0549 0.105 0.523 0.601 -0.151 0.261
danceability:liveness 0.2544 0.099 2.574 0.010 0.061 0.448
danceability:valence 0.0846 0.102 0.829 0.407 -0.115 0.285
danceability:tempo 0.0201 0.095 0.211 0.833 -0.166 0.206
danceability:duration_ms 0.0868 0.095 0.913 0.361 -0.100 0.273
danceability:artist_avg_popularity 0.1682 0.127 1.328 0.184 -0.080 0.416
danceability:artist_hit_rate -0.2407 0.118 -2.035 0.042 -0.472 -0.009
danceability:artist_n_tracks 0.2016 0.107 1.876 0.061 -0.009 0.412
danceability:playlist_avg_popularity 0.1502 0.126 1.193 0.233 -0.097 0.397
energy:speechiness 0.1085 0.118 0.920 0.358 -0.123 0.340
energy:acousticness -0.0548 0.092 -0.598 0.550 -0.234 0.125
energy:instrumentalness -0.0300 0.109 -0.276 0.782 -0.243 0.183
energy:liveness -0.0846 0.122 -0.693 0.488 -0.324 0.155
energy:valence -0.0815 0.119 -0.682 0.495 -0.316 0.153
energy:tempo -0.0266 0.114 -0.234 0.815 -0.249 0.196
energy:duration_ms -0.2561 0.107 -2.388 0.017 -0.466 -0.046
energy:artist_avg_popularity -0.2268 0.137 -1.659 0.097 -0.495 0.041
energy:artist_hit_rate -0.0689 0.139 -0.497 0.620 -0.341 0.203
energy:artist_n_tracks -0.0301 0.128 -0.236 0.814 -0.280 0.220
energy:playlist_avg_popularity 0.1602 0.149 1.074 0.283 -0.132 0.453
speechiness:acousticness -0.0341 0.111 -0.307 0.759 -0.252 0.184
speechiness:instrumentalness 0.0198 0.139 0.143 0.886 -0.252 0.291
speechiness:liveness 0.0632 0.091 0.692 0.489 -0.116 0.242
speechiness:valence -0.0681 0.110 -0.617 0.537 -0.284 0.148
speechiness:tempo 0.0481 0.084 0.574 0.566 -0.116 0.212
speechiness:duration_ms 0.0514 0.095 0.539 0.590 -0.135 0.238
speechiness:artist_avg_popularity -0.1873 0.113 -1.664 0.096 -0.408 0.033
speechiness:artist_hit_rate 0.0086 0.103 0.084 0.933 -0.194 0.211
speechiness:artist_n_tracks -0.1645 0.106 -1.559 0.119 -0.371 0.042
speechiness:playlist_avg_popularity 0.1579 0.126 1.257 0.209 -0.088 0.404
acousticness:instrumentalness 0.1266 0.115 1.098 0.272 -0.099 0.353
acousticness:liveness 0.0508 0.119 0.425 0.671 -0.183 0.285
acousticness:valence -0.1357 0.123 -1.101 0.271 -0.377 0.106
acousticness:tempo -0.0122 0.105 -0.116 0.908 -0.218 0.194
acousticness:duration_ms 0.0462 0.106 0.435 0.663 -0.162 0.254
acousticness:artist_avg_popularity -0.1642 0.136 -1.211 0.226 -0.430 0.102
acousticness:artist_hit_rate 0.0098 0.122 0.080 0.936 -0.229 0.248
acousticness:artist_n_tracks -0.1795 0.128 -1.407 0.159 -0.429 0.071
acousticness:playlist_avg_popularity -0.0606 0.148 -0.409 0.683 -0.351 0.230
instrumentalness:liveness -0.1387 0.099 -1.399 0.162 -0.333 0.056
instrumentalness:valence -0.0059 0.091 -0.064 0.949 -0.184 0.173
instrumentalness:tempo -0.0110 0.118 -0.093 0.926 -0.242 0.220
instrumentalness:duration_ms -0.0727 0.078 -0.934 0.350 -0.225 0.080
instrumentalness:artist_avg_popularity -0.1291 0.099 -1.310 0.190 -0.322 0.064
instrumentalness:artist_hit_rate 0.3146 0.220 1.433 0.152 -0.116 0.745
instrumentalness:artist_n_tracks 0.0251 0.118 0.212 0.832 -0.207 0.257
instrumentalness:playlist_avg_popularity -0.1883 0.121 -1.552 0.121 -0.426 0.049
liveness:valence -0.0132 0.106 -0.124 0.901 -0.222 0.195
liveness:tempo -0.0398 0.101 -0.395 0.693 -0.237 0.158
liveness:duration_ms 0.0909 0.095 0.959 0.338 -0.095 0.277
liveness:artist_avg_popularity -0.0716 0.113 -0.633 0.527 -0.293 0.150
liveness:artist_hit_rate -0.0180 0.108 -0.168 0.867 -0.229 0.193
liveness:artist_n_tracks 0.2350 0.098 2.387 0.017 0.042 0.428
liveness:playlist_avg_popularity -0.1615 0.109 -1.488 0.137 -0.374 0.051
valence:tempo -0.1527 0.114 -1.344 0.179 -0.375 0.070
valence:duration_ms -0.0291 0.098 -0.297 0.767 -0.221 0.163
valence:artist_avg_popularity -0.1838 0.116 -1.583 0.113 -0.411 0.044
valence:artist_hit_rate 0.1598 0.124 1.293 0.196 -0.082 0.402
valence:artist_n_tracks -0.1879 0.112 -1.683 0.092 -0.407 0.031
valence:playlist_avg_popularity 0.1540 0.124 1.246 0.213 -0.088 0.396
tempo:duration_ms 0.0027 0.058 0.046 0.964 -0.111 0.117
tempo:artist_avg_popularity 0.2137 0.117 1.832 0.067 -0.015 0.442
tempo:artist_hit_rate -0.0594 0.101 -0.589 0.556 -0.257 0.138
tempo:artist_n_tracks 0.0805 0.104 0.772 0.440 -0.124 0.285
tempo:playlist_avg_popularity -0.2858 0.123 -2.315 0.021 -0.528 -0.044
duration_ms:artist_avg_popularity -0.0373 0.107 -0.349 0.727 -0.247 0.172
duration_ms:artist_hit_rate -0.0298 0.125 -0.238 0.812 -0.275 0.216
duration_ms:artist_n_tracks -0.2413 0.103 -2.347 0.019 -0.443 -0.040
duration_ms:playlist_avg_popularity 0.1854 0.109 1.703 0.089 -0.028 0.399
artist_avg_popularity:artist_hit_rate 5.9261 0.411 14.417 0.000 5.120 6.732
artist_avg_popularity:artist_n_tracks 0.9351 0.155 6.016 0.000 0.630 1.240
artist_avg_popularity:playlist_avg_popularity 3.6629 0.081 45.434 0.000 3.505 3.821
artist_hit_rate:artist_n_tracks -0.3708 0.129 -2.874 0.004 -0.624 -0.118
artist_hit_rate:playlist_avg_popularity 0.3721 0.154 2.423 0.015 0.071 0.673
artist_n_tracks:playlist_avg_popularity 1.5321 0.117 13.143 0.000 1.304 1.761
==============================================================================
Omnibus: 1717.612 Durbin-Watson: 1.706
Prob(Omnibus): 0.000 Jarque-Bera (JB): 2784.162
Skew: -0.493 Prob(JB): 0.00
Kurtosis: 4.176 Cond. No. 16.4
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
How many coefficients were estimated?
m_5.params.size
92
How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?
m_5.params[m_5.pvalues < 0.05].size
21
WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?
m_5.params[m_5.pvalues < 0.05]
Intercept 35.526294 energy -0.479277 valence 0.222200 duration_ms 0.268506 artist_avg_popularity 17.134375 artist_hit_rate -3.211827 artist_n_tracks 0.254364 playlist_avg_popularity 8.989586 danceability:acousticness 0.262206 danceability:liveness 0.254387 danceability:artist_hit_rate -0.240670 energy:duration_ms -0.256102 liveness:artist_n_tracks 0.235014 tempo:playlist_avg_popularity -0.285812 duration_ms:artist_n_tracks -0.241334 artist_avg_popularity:artist_hit_rate 5.926103 artist_avg_popularity:artist_n_tracks 0.935135 artist_avg_popularity:playlist_avg_popularity 3.662950 artist_hit_rate:artist_n_tracks -0.370850 artist_hit_rate:playlist_avg_popularity 0.372104 artist_n_tracks:playlist_avg_popularity 1.532068 dtype: float64
Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?
m_5.params[m_5.pvalues < 0.05].sort_values(key=abs,ascending=False)[1:3]
artist_avg_popularity 17.134375 playlist_avg_popularity 8.989586 dtype: float64
Training performance
print(f'R squared: {m_5.rsquared}, RMSE: {m_5.mse_resid**0.5}')
R squared: 0.5819117497897595, RMSE: 15.348651962392772
viz_fitted_vs_actual(m_5.fittedvalues, spotify_model['track_popularity'], 'Continuous Model Additive with Interactions')
It is a bit better than the previous model. However, the main insight from this model the most significant features are artist_popularity and playlist_popularity. In addition, interaction between these two features with audio characteristics turned out to be significant as expected. Tracks by popular artists who have have higher hit rate will most likely have more popular tracks on average.
Continuous and Categorical Interaction¶
f_6 = f"track_popularity ~ artist_avg_popularity*(danceability + energy + speechiness + acousticness + instrumentalness + liveness + valence + tempo + duration_ms+ playlist_avg_popularity) + \
artist_avg_popularity*(artist_hit_rate + artist_n_tracks )+ artist_avg_popularity*({cat_features})+ playlist_avg_popularity*({cat_features})"
Interact the categorical inputs with the continuous inputs. This model must include the linear main effects as well (the formula interface helps with the interactions).
m_6 = fit_ols(f_6, spotify_model)
OLS Regression Results
==============================================================================
Dep. Variable: track_popularity R-squared: 0.586
Model: OLS Adj. R-squared: 0.584
Method: Least Squares F-statistic: 387.4
Date: Wed, 10 Dec 2025 Prob (F-statistic): 0.00
Time: 03:56:17 Log-Likelihood: -1.1749e+05
No. Observations: 28352 AIC: 2.352e+05
Df Residuals: 28248 BIC: 2.360e+05
Df Model: 103
Covariance Type: nonrobust
==========================================================================================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------------------------------------------------------------------
Intercept 37.4800 0.595 62.987 0.000 36.314 38.646
playlist_subgenre[T.big room] -1.1778 0.805 -1.463 0.143 -2.755 0.400
playlist_subgenre[T.classic rock] -0.6759 0.672 -1.006 0.315 -1.993 0.641
playlist_subgenre[T.dance pop] -2.5302 0.874 -2.895 0.004 -4.244 -0.817
playlist_subgenre[T.electro house] -1.4230 0.694 -2.050 0.040 -2.784 -0.062
playlist_subgenre[T.electropop] -1.3680 0.670 -2.041 0.041 -2.682 -0.054
playlist_subgenre[T.gangster rap] -2.4629 0.728 -3.381 0.001 -3.891 -1.035
playlist_subgenre[T.hard rock] -1.6392 0.692 -2.367 0.018 -2.996 -0.282
playlist_subgenre[T.hip hop] -3.2082 1.206 -2.661 0.008 -5.571 -0.845
playlist_subgenre[T.hip pop] -1.6616 0.785 -2.116 0.034 -3.200 -0.123
playlist_subgenre[T.indie poptimism] -1.5530 0.644 -2.410 0.016 -2.816 -0.290
playlist_subgenre[T.latin hip hop] -2.2785 0.708 -3.217 0.001 -3.667 -0.890
playlist_subgenre[T.latin pop] -2.7291 0.755 -3.614 0.000 -4.209 -1.249
playlist_subgenre[T.neo soul] -2.0773 0.687 -3.022 0.003 -3.425 -0.730
playlist_subgenre[T.new jack swing] -1.4588 0.973 -1.499 0.134 -3.367 0.449
playlist_subgenre[T.permanent wave] -2.7360 0.972 -2.815 0.005 -4.641 -0.831
playlist_subgenre[T.pop edm] -2.5417 0.723 -3.514 0.000 -3.959 -1.124
playlist_subgenre[T.post-teen pop] 0.3014 0.830 0.363 0.717 -1.326 1.929
playlist_subgenre[T.progressive electro house] -1.4377 0.781 -1.841 0.066 -2.968 0.093
playlist_subgenre[T.reggaeton] -3.9607 0.864 -4.582 0.000 -5.655 -2.266
playlist_subgenre[T.southern hip hop] -1.9978 0.661 -3.020 0.003 -3.294 -0.701
playlist_subgenre[T.trap] -5.1382 0.911 -5.637 0.000 -6.925 -3.352
playlist_subgenre[T.tropical] -3.4184 0.791 -4.320 0.000 -4.969 -1.868
playlist_subgenre[T.urban contemporary] -1.5708 0.731 -2.148 0.032 -3.004 -0.137
artist_avg_popularity 14.8130 0.693 21.372 0.000 13.455 16.172
artist_avg_popularity:playlist_subgenre[T.big room] 3.9477 0.819 4.819 0.000 2.342 5.553
artist_avg_popularity:playlist_subgenre[T.classic rock] 2.1470 0.765 2.807 0.005 0.648 3.646
artist_avg_popularity:playlist_subgenre[T.dance pop] 3.6069 1.017 3.546 0.000 1.613 5.601
artist_avg_popularity:playlist_subgenre[T.electro house] 2.4778 0.740 3.351 0.001 1.028 3.927
artist_avg_popularity:playlist_subgenre[T.electropop] 2.1709 0.674 3.219 0.001 0.849 3.493
artist_avg_popularity:playlist_subgenre[T.gangster rap] 1.6480 0.724 2.278 0.023 0.230 3.066
artist_avg_popularity:playlist_subgenre[T.hard rock] 4.7148 0.784 6.012 0.000 3.178 6.252
artist_avg_popularity:playlist_subgenre[T.hip hop] 3.6881 1.176 3.137 0.002 1.383 5.993
artist_avg_popularity:playlist_subgenre[T.hip pop] 3.3059 0.862 3.836 0.000 1.617 4.995
artist_avg_popularity:playlist_subgenre[T.indie poptimism] 2.1813 0.678 3.217 0.001 0.852 3.510
artist_avg_popularity:playlist_subgenre[T.latin hip hop] 1.9882 0.669 2.971 0.003 0.677 3.300
artist_avg_popularity:playlist_subgenre[T.latin pop] 2.1442 0.820 2.615 0.009 0.537 3.751
artist_avg_popularity:playlist_subgenre[T.neo soul] 1.4850 0.643 2.309 0.021 0.224 2.746
artist_avg_popularity:playlist_subgenre[T.new jack swing] 2.9153 0.828 3.521 0.000 1.292 4.538
artist_avg_popularity:playlist_subgenre[T.permanent wave] 5.0028 1.046 4.781 0.000 2.952 7.054
artist_avg_popularity:playlist_subgenre[T.pop edm] 0.9624 0.735 1.309 0.191 -0.479 2.403
artist_avg_popularity:playlist_subgenre[T.post-teen pop] 2.7488 0.894 3.076 0.002 0.997 4.500
artist_avg_popularity:playlist_subgenre[T.progressive electro house] 3.3523 0.657 5.101 0.000 2.064 4.640
artist_avg_popularity:playlist_subgenre[T.reggaeton] 1.2377 1.159 1.068 0.285 -1.034 3.509
artist_avg_popularity:playlist_subgenre[T.southern hip hop] 2.3091 0.726 3.180 0.001 0.886 3.733
artist_avg_popularity:playlist_subgenre[T.trap] 3.2798 1.061 3.090 0.002 1.199 5.360
artist_avg_popularity:playlist_subgenre[T.tropical] 6.4731 0.928 6.977 0.000 4.655 8.291
artist_avg_popularity:playlist_subgenre[T.urban contemporary] 1.3773 0.745 1.848 0.065 -0.084 2.838
danceability 0.3185 0.115 2.762 0.006 0.092 0.545
energy -0.3016 0.124 -2.437 0.015 -0.544 -0.059
speechiness 0.0667 0.108 0.619 0.536 -0.145 0.278
acousticness 0.0259 0.115 0.225 0.822 -0.200 0.252
instrumentalness -0.2796 0.106 -2.631 0.009 -0.488 -0.071
liveness -0.1035 0.094 -1.099 0.272 -0.288 0.081
valence 0.1240 0.111 1.121 0.262 -0.093 0.341
tempo 0.1202 0.095 1.262 0.207 -0.066 0.307
duration_ms 0.2192 0.103 2.137 0.033 0.018 0.420
playlist_avg_popularity 6.4515 0.602 10.715 0.000 5.271 7.632
playlist_avg_popularity:playlist_subgenre[T.big room] -1.1683 0.788 -1.482 0.138 -2.713 0.377
playlist_avg_popularity:playlist_subgenre[T.classic rock] 3.1587 0.842 3.751 0.000 1.508 4.809
playlist_avg_popularity:playlist_subgenre[T.dance pop] 2.1412 1.005 2.131 0.033 0.172 4.111
playlist_avg_popularity:playlist_subgenre[T.electro house] -0.7368 0.679 -1.086 0.278 -2.067 0.593
playlist_avg_popularity:playlist_subgenre[T.electropop] -1.8632 0.730 -2.554 0.011 -3.293 -0.433
playlist_avg_popularity:playlist_subgenre[T.gangster rap] -0.4371 0.871 -0.502 0.616 -2.144 1.270
playlist_avg_popularity:playlist_subgenre[T.hard rock] -0.1524 0.682 -0.224 0.823 -1.489 1.184
playlist_avg_popularity:playlist_subgenre[T.hip hop] 1.2189 1.366 0.892 0.372 -1.459 3.897
playlist_avg_popularity:playlist_subgenre[T.hip pop] -0.7359 0.942 -0.781 0.435 -2.582 1.111
playlist_avg_popularity:playlist_subgenre[T.indie poptimism] 0.7388 0.776 0.952 0.341 -0.782 2.260
playlist_avg_popularity:playlist_subgenre[T.latin hip hop] -1.8095 0.656 -2.760 0.006 -3.095 -0.524
playlist_avg_popularity:playlist_subgenre[T.latin pop] 1.3047 0.900 1.450 0.147 -0.459 3.068
playlist_avg_popularity:playlist_subgenre[T.neo soul] -0.7222 0.672 -1.074 0.283 -2.040 0.596
playlist_avg_popularity:playlist_subgenre[T.new jack swing] 1.5241 0.981 1.553 0.120 -0.399 3.448
playlist_avg_popularity:playlist_subgenre[T.permanent wave] 2.9793 1.146 2.600 0.009 0.734 5.225
playlist_avg_popularity:playlist_subgenre[T.pop edm] 0.1174 0.896 0.131 0.896 -1.638 1.873
playlist_avg_popularity:playlist_subgenre[T.post-teen pop] -0.3376 0.866 -0.390 0.697 -2.035 1.359
playlist_avg_popularity:playlist_subgenre[T.progressive electro house] -1.7776 0.660 -2.693 0.007 -3.071 -0.484
playlist_avg_popularity:playlist_subgenre[T.reggaeton] 2.9292 0.927 3.160 0.002 1.112 4.746
playlist_avg_popularity:playlist_subgenre[T.southern hip hop] 1.1845 0.857 1.383 0.167 -0.495 2.864
playlist_avg_popularity:playlist_subgenre[T.trap] 2.5120 1.144 2.196 0.028 0.270 4.754
playlist_avg_popularity:playlist_subgenre[T.tropical] 0.0481 1.377 0.035 0.972 -2.651 2.748
playlist_avg_popularity:playlist_subgenre[T.urban contemporary] 0.1396 0.843 0.166 0.868 -1.513 1.792
artist_avg_popularity:danceability 0.1957 0.118 1.665 0.096 -0.035 0.426
artist_avg_popularity:energy -0.3158 0.124 -2.544 0.011 -0.559 -0.073
artist_avg_popularity:speechiness -0.1267 0.112 -1.135 0.257 -0.346 0.092
artist_avg_popularity:acousticness -0.0423 0.117 -0.360 0.718 -0.272 0.188
artist_avg_popularity:instrumentalness -0.1551 0.090 -1.715 0.086 -0.332 0.022
artist_avg_popularity:liveness -0.0554 0.093 -0.595 0.552 -0.238 0.127
artist_avg_popularity:valence -0.0317 0.106 -0.299 0.765 -0.240 0.176
artist_avg_popularity:tempo 0.0656 0.089 0.735 0.462 -0.109 0.240
artist_avg_popularity:duration_ms -0.0286 0.090 -0.318 0.751 -0.205 0.148
artist_avg_popularity:playlist_avg_popularity 3.0286 0.102 29.734 0.000 2.829 3.228
artist_hit_rate -3.3339 0.327 -10.193 0.000 -3.975 -2.693
artist_n_tracks 0.2009 0.130 1.542 0.123 -0.055 0.456
artist_avg_popularity:artist_hit_rate 6.0193 0.374 16.097 0.000 5.286 6.752
artist_avg_popularity:artist_n_tracks 1.8025 0.147 12.240 0.000 1.514 2.091
mode 0.1398 0.189 0.740 0.459 -0.230 0.510
artist_n_genres -0.5382 0.159 -3.382 0.001 -0.850 -0.226
key 0.0006 0.026 0.025 0.980 -0.050 0.051
artist_avg_popularity:mode -0.3316 0.220 -1.509 0.131 -0.762 0.099
artist_avg_popularity:artist_n_genres 0.3579 0.260 1.377 0.168 -0.151 0.867
artist_avg_popularity:key 0.0140 0.030 0.467 0.640 -0.045 0.073
playlist_avg_popularity:mode 0.2001 0.218 0.918 0.359 -0.227 0.627
playlist_avg_popularity:artist_n_genres 1.5433 0.118 13.127 0.000 1.313 1.774
playlist_avg_popularity:key -0.0018 0.030 -0.061 0.952 -0.060 0.056
==============================================================================
Omnibus: 1644.834 Durbin-Watson: 1.715
Prob(Omnibus): 0.000 Jarque-Bera (JB): 2724.593
Skew: -0.470 Prob(JB): 0.00
Kurtosis: 4.192 Cond. No. 298.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
my_coefplot(m_6, figsize_use=(12,30))
How many coefficients were estimated?
m_6.params.size
104
How many coefficients (and thus features) are STATISTICALLY SIGNIFICANT using commonly accepted thresholds?
m_6.params[m_6.pvalues < 0.05].size
60
WHICH coefficients (and thus features) are STATISTICALLY SIGNIFICANT and what are the coefficients POSITIVE or NEGATIVE for those features?
m_6.params[m_6.pvalues < 0.05].sort_values(key=abs,ascending=False)
Intercept 37.480028 artist_avg_popularity 14.813024 artist_avg_popularity:playlist_subgenre[T.tropical] 6.473092 playlist_avg_popularity 6.451494 artist_avg_popularity:artist_hit_rate 6.019263 playlist_subgenre[T.trap] -5.138187 artist_avg_popularity:playlist_subgenre[T.permanent wave] 5.002814 artist_avg_popularity:playlist_subgenre[T.hard rock] 4.714800 playlist_subgenre[T.reggaeton] -3.960673 artist_avg_popularity:playlist_subgenre[T.big room] 3.947721 artist_avg_popularity:playlist_subgenre[T.hip hop] 3.688101 artist_avg_popularity:playlist_subgenre[T.dance pop] 3.606861 playlist_subgenre[T.tropical] -3.418394 artist_avg_popularity:playlist_subgenre[T.progressive electro house] 3.352253 artist_hit_rate -3.333921 artist_avg_popularity:playlist_subgenre[T.hip pop] 3.305906 artist_avg_popularity:playlist_subgenre[T.trap] 3.279850 playlist_subgenre[T.hip hop] -3.208179 playlist_avg_popularity:playlist_subgenre[T.classic rock] 3.158703 artist_avg_popularity:playlist_avg_popularity 3.028626 playlist_avg_popularity:playlist_subgenre[T.permanent wave] 2.979330 playlist_avg_popularity:playlist_subgenre[T.reggaeton] 2.929237 artist_avg_popularity:playlist_subgenre[T.new jack swing] 2.915261 artist_avg_popularity:playlist_subgenre[T.post-teen pop] 2.748823 playlist_subgenre[T.permanent wave] -2.736028 playlist_subgenre[T.latin pop] -2.729084 playlist_subgenre[T.pop edm] -2.541709 playlist_subgenre[T.dance pop] -2.530190 playlist_avg_popularity:playlist_subgenre[T.trap] 2.511971 artist_avg_popularity:playlist_subgenre[T.electro house] 2.477782 playlist_subgenre[T.gangster rap] -2.462878 artist_avg_popularity:playlist_subgenre[T.southern hip hop] 2.309143 playlist_subgenre[T.latin hip hop] -2.278549 artist_avg_popularity:playlist_subgenre[T.indie poptimism] 2.181290 artist_avg_popularity:playlist_subgenre[T.electropop] 2.170879 artist_avg_popularity:playlist_subgenre[T.classic rock] 2.146995 artist_avg_popularity:playlist_subgenre[T.latin pop] 2.144192 playlist_avg_popularity:playlist_subgenre[T.dance pop] 2.141230 playlist_subgenre[T.neo soul] -2.077257 playlist_subgenre[T.southern hip hop] -1.997831 artist_avg_popularity:playlist_subgenre[T.latin hip hop] 1.988158 playlist_avg_popularity:playlist_subgenre[T.electropop] -1.863152 playlist_avg_popularity:playlist_subgenre[T.latin hip hop] -1.809542 artist_avg_popularity:artist_n_tracks 1.802462 playlist_avg_popularity:playlist_subgenre[T.progressive electro house] -1.777596 playlist_subgenre[T.hip pop] -1.661564 artist_avg_popularity:playlist_subgenre[T.gangster rap] 1.647973 playlist_subgenre[T.hard rock] -1.639171 playlist_subgenre[T.urban contemporary] -1.570840 playlist_subgenre[T.indie poptimism] -1.553003 playlist_avg_popularity:artist_n_genres 1.543339 artist_avg_popularity:playlist_subgenre[T.neo soul] 1.485005 playlist_subgenre[T.electro house] -1.422950 playlist_subgenre[T.electropop] -1.368048 artist_n_genres -0.538173 danceability 0.318542 artist_avg_popularity:energy -0.315795 energy -0.301609 instrumentalness -0.279625 duration_ms 0.219213 dtype: float64
Which two STATISTICALLY SIGNIFICANT coefficients (and thus features) have the highest MAGNITUDE coefficient values?
m_6.params[m_6.pvalues < 0.05].sort_values(ascending=False)[1:3]
artist_avg_popularity 14.813024 artist_avg_popularity:playlist_subgenre[T.tropical] 6.473092 dtype: float64
print(f'R squared: {m_6.rsquared}, RMSE: {m_6.mse_resid**0.5}')
R squared: 0.5855224680078064, RMSE: 15.285476449238704
viz_fitted_vs_actual(m_6.fittedvalues, spotify_model['track_popularity'], 'Final Model with Interactions')
This is the best model so far.
The main insight that is derived is that the interaction between the genres and artist popularity along with characteristic features of a popular song such as danceability, energy, or instrumantelness are significant features of track popularity.
Polynomials¶
f_7 = "track_popularity ~ \
(artist_avg_popularity + playlist_avg_popularity + danceability + energy + valence + \
tempo + duration_ms + artist_hit_rate + artist_n_tracks)*playlist_subgenre + \
(I(artist_avg_popularity**2) + I(playlist_avg_popularity**2) + I(danceability**2) + I(energy**2) + \
I(valence**2) + I(tempo**2) + I(duration_ms**2) + \
I(artist_hit_rate**2) + I(artist_n_tracks**2))*playlist_subgenre"
m_7 = fit_ols(f_7, spotify_model)
OLS Regression Results
==============================================================================
Dep. Variable: track_popularity R-squared: 0.624
Model: OLS Adj. R-squared: 0.618
Method: Least Squares F-statistic: 101.7
Date: Wed, 10 Dec 2025 Prob (F-statistic): 0.00
Time: 03:59:10 Log-Likelihood: -1.1611e+05
No. Observations: 28352 AIC: 2.331e+05
Df Residuals: 27896 BIC: 2.369e+05
Df Model: 455
Covariance Type: nonrobust
==================================================================================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------------------------------------------------------------------------
Intercept 36.2646 1.180 30.732 0.000 33.952 38.578
playlist_subgenre[T.big room] -1.9686 2.076 -0.948 0.343 -6.038 2.101
playlist_subgenre[T.classic rock] -4.2232 1.749 -2.415 0.016 -7.651 -0.796
playlist_subgenre[T.dance pop] 1.2536 1.664 0.753 0.451 -2.009 4.516
playlist_subgenre[T.electro house] -1.9996 1.888 -1.059 0.290 -5.701 1.701
playlist_subgenre[T.electropop] -4.8804 1.563 -3.122 0.002 -7.944 -1.816
playlist_subgenre[T.gangster rap] -3.2760 1.689 -1.940 0.052 -6.586 0.034
playlist_subgenre[T.hard rock] -1.1324 1.810 -0.626 0.531 -4.679 2.414
playlist_subgenre[T.hip hop] -2.3408 2.752 -0.851 0.395 -7.735 3.053
playlist_subgenre[T.hip pop] -2.6534 1.899 -1.397 0.162 -6.376 1.069
playlist_subgenre[T.indie poptimism] -4.7762 1.517 -3.148 0.002 -7.750 -1.802
playlist_subgenre[T.latin hip hop] -2.5177 1.681 -1.498 0.134 -5.813 0.778
playlist_subgenre[T.latin pop] -5.9494 1.719 -3.461 0.001 -9.319 -2.580
playlist_subgenre[T.neo soul] -2.9108 1.597 -1.823 0.068 -6.040 0.219
playlist_subgenre[T.new jack swing] 0.0539 2.322 0.023 0.981 -4.498 4.606
playlist_subgenre[T.permanent wave] -3.6638 1.815 -2.018 0.044 -7.222 -0.105
playlist_subgenre[T.pop edm] -7.8114 1.693 -4.614 0.000 -11.130 -4.493
playlist_subgenre[T.post-teen pop] -3.6794 1.827 -2.014 0.044 -7.261 -0.098
playlist_subgenre[T.progressive electro house] -2.4637 1.824 -1.351 0.177 -6.039 1.111
playlist_subgenre[T.reggaeton] -5.6652 2.669 -2.122 0.034 -10.897 -0.433
playlist_subgenre[T.southern hip hop] -3.5135 1.655 -2.122 0.034 -6.758 -0.269
playlist_subgenre[T.trap] -8.4319 1.863 -4.527 0.000 -12.083 -4.781
playlist_subgenre[T.tropical] -3.5891 1.741 -2.061 0.039 -7.002 -0.176
playlist_subgenre[T.urban contemporary] -4.2484 1.747 -2.432 0.015 -7.672 -0.824
artist_avg_popularity 19.5773 1.165 16.807 0.000 17.294 21.860
artist_avg_popularity:playlist_subgenre[T.big room] 0.3686 1.760 0.209 0.834 -3.082 3.819
artist_avg_popularity:playlist_subgenre[T.classic rock] 1.8892 1.609 1.174 0.240 -1.264 5.043
artist_avg_popularity:playlist_subgenre[T.dance pop] 2.4527 1.691 1.451 0.147 -0.861 5.766
artist_avg_popularity:playlist_subgenre[T.electro house] 1.7105 1.630 1.050 0.294 -1.484 4.905
artist_avg_popularity:playlist_subgenre[T.electropop] 4.6163 1.581 2.920 0.004 1.517 7.715
artist_avg_popularity:playlist_subgenre[T.gangster rap] 5.6255 1.534 3.668 0.000 2.620 8.631
artist_avg_popularity:playlist_subgenre[T.hard rock] 7.3557 1.542 4.769 0.000 4.333 10.379
artist_avg_popularity:playlist_subgenre[T.hip hop] 2.3611 1.733 1.363 0.173 -1.035 5.757
artist_avg_popularity:playlist_subgenre[T.hip pop] 3.6749 1.771 2.075 0.038 0.203 7.146
artist_avg_popularity:playlist_subgenre[T.indie poptimism] 3.9784 1.477 2.694 0.007 1.084 6.873
artist_avg_popularity:playlist_subgenre[T.latin hip hop] 2.9650 1.567 1.892 0.058 -0.106 6.036
artist_avg_popularity:playlist_subgenre[T.latin pop] 5.7313 1.718 3.336 0.001 2.364 9.099
artist_avg_popularity:playlist_subgenre[T.neo soul] 3.1149 1.480 2.104 0.035 0.213 6.017
artist_avg_popularity:playlist_subgenre[T.new jack swing] 1.3678 1.713 0.799 0.425 -1.990 4.725
artist_avg_popularity:playlist_subgenre[T.permanent wave] 1.2060 1.621 0.744 0.457 -1.971 4.383
artist_avg_popularity:playlist_subgenre[T.pop edm] 4.4241 1.818 2.434 0.015 0.861 7.987
artist_avg_popularity:playlist_subgenre[T.post-teen pop] 2.5478 1.720 1.482 0.138 -0.823 5.918
artist_avg_popularity:playlist_subgenre[T.progressive electro house] -1.5750 1.489 -1.058 0.290 -4.493 1.343
artist_avg_popularity:playlist_subgenre[T.reggaeton] 3.3175 2.256 1.471 0.141 -1.104 7.739
artist_avg_popularity:playlist_subgenre[T.southern hip hop] 4.0749 1.504 2.709 0.007 1.126 7.024
artist_avg_popularity:playlist_subgenre[T.trap] 5.8081 1.780 3.262 0.001 2.318 9.298
artist_avg_popularity:playlist_subgenre[T.tropical] 7.2145 1.643 4.391 0.000 3.994 10.435
artist_avg_popularity:playlist_subgenre[T.urban contemporary] 3.7987 1.609 2.362 0.018 0.646 6.951
playlist_avg_popularity 9.8344 0.731 13.446 0.000 8.401 11.268
playlist_avg_popularity:playlist_subgenre[T.big room] -0.4623 1.680 -0.275 0.783 -3.756 2.831
playlist_avg_popularity:playlist_subgenre[T.classic rock] 1.4046 0.977 1.438 0.150 -0.510 3.319
playlist_avg_popularity:playlist_subgenre[T.dance pop] -10.0526 2.487 -4.042 0.000 -14.927 -5.178
playlist_avg_popularity:playlist_subgenre[T.electro house] -2.1951 1.450 -1.513 0.130 -5.038 0.648
playlist_avg_popularity:playlist_subgenre[T.electropop] -0.7383 0.993 -0.744 0.457 -2.684 1.208
playlist_avg_popularity:playlist_subgenre[T.gangster rap] -1.4846 1.169 -1.269 0.204 -3.777 0.808
playlist_avg_popularity:playlist_subgenre[T.hard rock] -2.0350 1.167 -1.743 0.081 -4.323 0.253
playlist_avg_popularity:playlist_subgenre[T.hip hop] -4.0025 4.820 -0.830 0.406 -13.449 5.444
playlist_avg_popularity:playlist_subgenre[T.hip pop] -4.9599 1.129 -4.394 0.000 -7.172 -2.747
playlist_avg_popularity:playlist_subgenre[T.indie poptimism] -1.2618 0.941 -1.341 0.180 -3.106 0.582
playlist_avg_popularity:playlist_subgenre[T.latin hip hop] -4.6586 1.054 -4.418 0.000 -6.725 -2.592
playlist_avg_popularity:playlist_subgenre[T.latin pop] -4.1698 1.303 -3.201 0.001 -6.723 -1.616
playlist_avg_popularity:playlist_subgenre[T.neo soul] -2.5274 1.119 -2.258 0.024 -4.721 -0.334
playlist_avg_popularity:playlist_subgenre[T.new jack swing] 1.5423 2.086 0.740 0.460 -2.546 5.630
playlist_avg_popularity:playlist_subgenre[T.permanent wave] -3.2505 2.649 -1.227 0.220 -8.443 1.942
playlist_avg_popularity:playlist_subgenre[T.pop edm] -0.3464 1.057 -0.328 0.743 -2.417 1.725
playlist_avg_popularity:playlist_subgenre[T.post-teen pop] -2.9509 1.121 -2.633 0.008 -5.147 -0.754
playlist_avg_popularity:playlist_subgenre[T.progressive electro house] -1.0256 1.278 -0.803 0.422 -3.530 1.478
playlist_avg_popularity:playlist_subgenre[T.reggaeton] 3.1093 1.096 2.838 0.005 0.962 5.257
playlist_avg_popularity:playlist_subgenre[T.southern hip hop] 1.1486 1.113 1.032 0.302 -1.033 3.330
playlist_avg_popularity:playlist_subgenre[T.trap] -0.8049 2.247 -0.358 0.720 -5.210 3.600
playlist_avg_popularity:playlist_subgenre[T.tropical] -1.7753 1.571 -1.130 0.258 -4.854 1.303
playlist_avg_popularity:playlist_subgenre[T.urban contemporary] -2.0328 1.005 -2.023 0.043 -4.003 -0.063
danceability 1.6226 0.894 1.816 0.069 -0.129 3.374
danceability:playlist_subgenre[T.big room] -2.3248 1.204 -1.931 0.054 -4.685 0.035
danceability:playlist_subgenre[T.classic rock] -0.4456 1.233 -0.361 0.718 -2.862 1.970
danceability:playlist_subgenre[T.dance pop] -1.1411 1.112 -1.026 0.305 -3.321 1.039
danceability:playlist_subgenre[T.electro house] -2.3115 1.082 -2.136 0.033 -4.433 -0.190
danceability:playlist_subgenre[T.electropop] -1.6433 1.119 -1.469 0.142 -3.836 0.549
danceability:playlist_subgenre[T.gangster rap] -2.2548 1.067 -2.112 0.035 -4.347 -0.163
danceability:playlist_subgenre[T.hard rock] 1.0370 1.503 0.690 0.490 -1.909 3.983
danceability:playlist_subgenre[T.hip hop] -0.7775 1.049 -0.741 0.458 -2.833 1.278
danceability:playlist_subgenre[T.hip pop] -1.1696 1.137 -1.028 0.304 -3.399 1.060
danceability:playlist_subgenre[T.indie poptimism] -1.4242 1.089 -1.308 0.191 -3.558 0.709
danceability:playlist_subgenre[T.latin hip hop] -2.2554 1.148 -1.964 0.050 -4.506 -0.005
danceability:playlist_subgenre[T.latin pop] 1.2333 1.123 1.098 0.272 -0.968 3.435
danceability:playlist_subgenre[T.neo soul] -1.6799 1.047 -1.604 0.109 -3.733 0.373
danceability:playlist_subgenre[T.new jack swing] -2.5732 1.265 -2.035 0.042 -5.052 -0.095
danceability:playlist_subgenre[T.permanent wave] -0.8456 1.326 -0.638 0.524 -3.445 1.754
danceability:playlist_subgenre[T.pop edm] -1.6741 1.168 -1.433 0.152 -3.963 0.615
danceability:playlist_subgenre[T.post-teen pop] -0.6312 1.130 -0.559 0.576 -2.845 1.583
danceability:playlist_subgenre[T.progressive electro house] -1.4940 1.090 -1.371 0.170 -3.630 0.642
danceability:playlist_subgenre[T.reggaeton] -0.1228 1.571 -0.078 0.938 -3.201 2.956
danceability:playlist_subgenre[T.southern hip hop] -0.9601 1.002 -0.958 0.338 -2.925 1.004
danceability:playlist_subgenre[T.trap] -1.0850 1.094 -0.992 0.321 -3.229 1.059
danceability:playlist_subgenre[T.tropical] -0.9816 1.154 -0.850 0.395 -3.244 1.281
danceability:playlist_subgenre[T.urban contemporary] -1.1758 1.053 -1.117 0.264 -3.239 0.887
energy -0.5055 0.581 -0.869 0.385 -1.645 0.634
energy:playlist_subgenre[T.big room] 0.3530 1.214 0.291 0.771 -2.027 2.733
energy:playlist_subgenre[T.classic rock] -0.3857 0.817 -0.472 0.637 -1.987 1.216
energy:playlist_subgenre[T.dance pop] -1.1515 0.847 -1.359 0.174 -2.812 0.509
energy:playlist_subgenre[T.electro house] 0.1184 0.812 0.146 0.884 -1.473 1.710
energy:playlist_subgenre[T.electropop] 0.6571 0.835 0.787 0.431 -0.980 2.294
energy:playlist_subgenre[T.gangster rap] 0.9175 0.861 1.065 0.287 -0.771 2.606
energy:playlist_subgenre[T.hard rock] -1.2571 0.844 -1.489 0.136 -2.911 0.397
energy:playlist_subgenre[T.hip hop] 0.0197 0.940 0.021 0.983 -1.824 1.863
energy:playlist_subgenre[T.hip pop] -0.1709 1.047 -0.163 0.870 -2.222 1.880
energy:playlist_subgenre[T.indie poptimism] -0.1758 0.840 -0.209 0.834 -1.821 1.470
energy:playlist_subgenre[T.latin hip hop] 0.0308 0.854 0.036 0.971 -1.644 1.705
energy:playlist_subgenre[T.latin pop] 0.1807 0.907 0.199 0.842 -1.597 1.959
energy:playlist_subgenre[T.neo soul] -0.3800 0.923 -0.412 0.681 -2.189 1.429
energy:playlist_subgenre[T.new jack swing] -1.2141 0.897 -1.354 0.176 -2.972 0.543
energy:playlist_subgenre[T.permanent wave] 1.2217 0.859 1.423 0.155 -0.461 2.905
energy:playlist_subgenre[T.pop edm] 0.1014 0.943 0.108 0.914 -1.747 1.950
energy:playlist_subgenre[T.post-teen pop] 0.0577 0.897 0.064 0.949 -1.701 1.816
energy:playlist_subgenre[T.progressive electro house] -0.1027 0.917 -0.112 0.911 -1.900 1.695
energy:playlist_subgenre[T.reggaeton] 1.2551 1.256 0.999 0.318 -1.208 3.718
energy:playlist_subgenre[T.southern hip hop] -0.2111 0.823 -0.257 0.797 -1.823 1.401
energy:playlist_subgenre[T.trap] 1.7872 0.885 2.019 0.044 0.052 3.522
energy:playlist_subgenre[T.tropical] 0.3020 0.899 0.336 0.737 -1.461 2.065
energy:playlist_subgenre[T.urban contemporary] -1.0285 0.960 -1.072 0.284 -2.909 0.852
valence -0.3394 0.610 -0.556 0.578 -1.536 0.857
valence:playlist_subgenre[T.big room] 0.2195 1.142 0.192 0.848 -2.020 2.459
valence:playlist_subgenre[T.classic rock] -0.7716 0.902 -0.856 0.392 -2.539 0.996
valence:playlist_subgenre[T.dance pop] 1.0169 0.806 1.262 0.207 -0.563 2.596
valence:playlist_subgenre[T.electro house] 1.0694 0.782 1.367 0.171 -0.463 2.602
valence:playlist_subgenre[T.electropop] -0.3087 0.793 -0.389 0.697 -1.864 1.246
valence:playlist_subgenre[T.gangster rap] -0.0329 0.778 -0.042 0.966 -1.557 1.492
valence:playlist_subgenre[T.hard rock] -0.9597 0.877 -1.094 0.274 -2.679 0.760
valence:playlist_subgenre[T.hip hop] 0.1490 0.787 0.189 0.850 -1.394 1.692
valence:playlist_subgenre[T.hip pop] 1.7761 0.874 2.033 0.042 0.064 3.489
valence:playlist_subgenre[T.indie poptimism] -0.3856 0.796 -0.485 0.628 -1.945 1.174
valence:playlist_subgenre[T.latin hip hop] 0.1610 0.818 0.197 0.844 -1.443 1.765
valence:playlist_subgenre[T.latin pop] -0.8767 0.884 -0.992 0.321 -2.609 0.856
valence:playlist_subgenre[T.neo soul] 0.7968 0.805 0.989 0.322 -0.782 2.375
valence:playlist_subgenre[T.new jack swing] 0.2522 1.036 0.243 0.808 -1.779 2.284
valence:playlist_subgenre[T.permanent wave] 0.6348 0.871 0.729 0.466 -1.073 2.343
valence:playlist_subgenre[T.pop edm] -0.5850 0.893 -0.655 0.512 -2.335 1.165
valence:playlist_subgenre[T.post-teen pop] 0.5247 0.880 0.596 0.551 -1.199 2.249
valence:playlist_subgenre[T.progressive electro house] 0.5102 0.805 0.634 0.526 -1.067 2.087
valence:playlist_subgenre[T.reggaeton] 1.2511 1.212 1.032 0.302 -1.124 3.627
valence:playlist_subgenre[T.southern hip hop] 0.7485 0.764 0.979 0.328 -0.750 2.247
valence:playlist_subgenre[T.trap] 0.6157 0.843 0.731 0.465 -1.036 2.268
valence:playlist_subgenre[T.tropical] 0.4230 0.802 0.528 0.598 -1.148 1.994
valence:playlist_subgenre[T.urban contemporary] 2.3839 0.828 2.878 0.004 0.760 4.007
tempo -0.0591 0.470 -0.126 0.900 -0.979 0.861
tempo:playlist_subgenre[T.big room] 0.0807 1.148 0.070 0.944 -2.170 2.332
tempo:playlist_subgenre[T.classic rock] 0.3480 0.671 0.519 0.604 -0.967 1.663
tempo:playlist_subgenre[T.dance pop] 0.6100 0.734 0.831 0.406 -0.830 2.049
tempo:playlist_subgenre[T.electro house] 0.9172 1.134 0.809 0.419 -1.305 3.140
tempo:playlist_subgenre[T.electropop] 0.0171 0.693 0.025 0.980 -1.342 1.376
tempo:playlist_subgenre[T.gangster rap] 0.3685 0.587 0.627 0.531 -0.783 1.520
tempo:playlist_subgenre[T.hard rock] 0.6169 0.637 0.969 0.332 -0.631 1.865
tempo:playlist_subgenre[T.hip hop] 0.0629 0.585 0.108 0.914 -1.084 1.210
tempo:playlist_subgenre[T.hip pop] -0.1897 0.683 -0.278 0.781 -1.528 1.148
tempo:playlist_subgenre[T.indie poptimism] 0.7297 0.614 1.189 0.235 -0.473 1.933
tempo:playlist_subgenre[T.latin hip hop] 1.1915 0.661 1.801 0.072 -0.105 2.488
tempo:playlist_subgenre[T.latin pop] 0.1781 0.642 0.277 0.782 -1.081 1.437
tempo:playlist_subgenre[T.neo soul] 0.2423 0.605 0.400 0.689 -0.944 1.428
tempo:playlist_subgenre[T.new jack swing] -0.6436 0.695 -0.925 0.355 -2.007 0.720
tempo:playlist_subgenre[T.permanent wave] -0.2020 0.687 -0.294 0.769 -1.548 1.144
tempo:playlist_subgenre[T.pop edm] 0.5796 0.764 0.759 0.448 -0.917 2.076
tempo:playlist_subgenre[T.post-teen pop] -0.6075 0.669 -0.909 0.364 -1.918 0.703
tempo:playlist_subgenre[T.progressive electro house] 0.3652 1.243 0.294 0.769 -2.071 2.801
tempo:playlist_subgenre[T.reggaeton] 1.3165 0.753 1.747 0.081 -0.160 2.793
tempo:playlist_subgenre[T.southern hip hop] -0.3997 0.565 -0.708 0.479 -1.507 0.708
tempo:playlist_subgenre[T.trap] -0.3197 0.646 -0.495 0.620 -1.585 0.946
tempo:playlist_subgenre[T.tropical] 0.4166 0.724 0.576 0.565 -1.002 1.835
tempo:playlist_subgenre[T.urban contemporary] 0.0308 0.619 0.050 0.960 -1.182 1.243
duration_ms 1.1862 0.446 2.663 0.008 0.313 2.059
duration_ms:playlist_subgenre[T.big room] -1.3682 0.784 -1.745 0.081 -2.905 0.169
duration_ms:playlist_subgenre[T.classic rock] -1.3732 0.746 -1.840 0.066 -2.836 0.090
duration_ms:playlist_subgenre[T.dance pop] -0.8326 0.760 -1.095 0.273 -2.322 0.657
duration_ms:playlist_subgenre[T.electro house] -2.3545 0.587 -4.014 0.000 -3.504 -1.205
duration_ms:playlist_subgenre[T.electropop] -1.1286 0.708 -1.595 0.111 -2.516 0.258
duration_ms:playlist_subgenre[T.gangster rap] -1.1543 0.647 -1.784 0.074 -2.423 0.114
duration_ms:playlist_subgenre[T.hard rock] -0.8823 0.746 -1.183 0.237 -2.344 0.579
duration_ms:playlist_subgenre[T.hip hop] 1.0978 0.789 1.391 0.164 -0.449 2.644
duration_ms:playlist_subgenre[T.hip pop] -1.2588 0.840 -1.498 0.134 -2.906 0.388
duration_ms:playlist_subgenre[T.indie poptimism] -0.3919 0.742 -0.529 0.597 -1.845 1.061
duration_ms:playlist_subgenre[T.latin hip hop] -1.0417 0.652 -1.597 0.110 -2.320 0.237
duration_ms:playlist_subgenre[T.latin pop] -1.4729 0.858 -1.716 0.086 -3.155 0.209
duration_ms:playlist_subgenre[T.neo soul] -1.0260 0.612 -1.677 0.094 -2.225 0.173
duration_ms:playlist_subgenre[T.new jack swing] -0.1686 0.842 -0.200 0.841 -1.819 1.482
duration_ms:playlist_subgenre[T.permanent wave] -1.2799 0.762 -1.680 0.093 -2.773 0.213
duration_ms:playlist_subgenre[T.pop edm] -2.3247 0.830 -2.801 0.005 -3.951 -0.698
duration_ms:playlist_subgenre[T.post-teen pop] -1.2095 0.936 -1.292 0.196 -3.044 0.625
duration_ms:playlist_subgenre[T.progressive electro house] -2.3513 0.719 -3.268 0.001 -3.762 -0.941
duration_ms:playlist_subgenre[T.reggaeton] 0.7129 0.955 0.746 0.456 -1.160 2.585
duration_ms:playlist_subgenre[T.southern hip hop] -0.6858 0.603 -1.136 0.256 -1.869 0.497
duration_ms:playlist_subgenre[T.trap] -1.0799 0.737 -1.464 0.143 -2.525 0.365
duration_ms:playlist_subgenre[T.tropical] -1.0692 0.747 -1.432 0.152 -2.533 0.394
duration_ms:playlist_subgenre[T.urban contemporary] -0.6038 0.659 -0.917 0.359 -1.895 0.687
artist_hit_rate -1.4088 1.217 -1.158 0.247 -3.794 0.976
artist_hit_rate:playlist_subgenre[T.big room] -5.5373 2.295 -2.412 0.016 -10.036 -1.038
artist_hit_rate:playlist_subgenre[T.classic rock] 0.9750 1.669 0.584 0.559 -2.296 4.246
artist_hit_rate:playlist_subgenre[T.dance pop] 1.4477 1.552 0.933 0.351 -1.594 4.490
artist_hit_rate:playlist_subgenre[T.electro house] -0.6717 2.134 -0.315 0.753 -4.855 3.511
artist_hit_rate:playlist_subgenre[T.electropop] -1.1850 1.544 -0.767 0.443 -4.212 1.842
artist_hit_rate:playlist_subgenre[T.gangster rap] -3.6611 1.644 -2.227 0.026 -6.884 -0.439
artist_hit_rate:playlist_subgenre[T.hard rock] -2.9241 1.685 -1.736 0.083 -6.226 0.378
artist_hit_rate:playlist_subgenre[T.hip hop] 0.1033 1.555 0.066 0.947 -2.944 3.151
artist_hit_rate:playlist_subgenre[T.hip pop] 4.9828 1.774 2.809 0.005 1.506 8.460
artist_hit_rate:playlist_subgenre[T.indie poptimism] -0.5269 1.544 -0.341 0.733 -3.554 2.500
artist_hit_rate:playlist_subgenre[T.latin hip hop] 2.3650 1.630 1.451 0.147 -0.830 5.560
artist_hit_rate:playlist_subgenre[T.latin pop] 2.3601 1.554 1.519 0.129 -0.686 5.406
artist_hit_rate:playlist_subgenre[T.neo soul] -2.0838 1.668 -1.249 0.212 -5.353 1.185
artist_hit_rate:playlist_subgenre[T.new jack swing] -0.4752 2.230 -0.213 0.831 -4.846 3.895
artist_hit_rate:playlist_subgenre[T.permanent wave] 2.1571 1.613 1.338 0.181 -1.004 5.318
artist_hit_rate:playlist_subgenre[T.pop edm] -2.8291 1.686 -1.678 0.093 -6.133 0.475
artist_hit_rate:playlist_subgenre[T.post-teen pop] 3.6934 1.602 2.305 0.021 0.553 6.834
artist_hit_rate:playlist_subgenre[T.progressive electro house] -0.7408 1.979 -0.374 0.708 -4.620 3.139
artist_hit_rate:playlist_subgenre[T.reggaeton] -2.5181 1.791 -1.406 0.160 -6.028 0.991
artist_hit_rate:playlist_subgenre[T.southern hip hop] 1.1692 1.582 0.739 0.460 -1.931 4.270
artist_hit_rate:playlist_subgenre[T.trap] -1.9553 1.630 -1.200 0.230 -5.150 1.239
artist_hit_rate:playlist_subgenre[T.tropical] -0.6383 1.903 -0.335 0.737 -4.368 3.091
artist_hit_rate:playlist_subgenre[T.urban contemporary] -1.2168 1.538 -0.791 0.429 -4.231 1.797
artist_n_tracks 1.0025 0.652 1.538 0.124 -0.275 2.280
artist_n_tracks:playlist_subgenre[T.big room] 0.5712 0.866 0.659 0.510 -1.126 2.269
artist_n_tracks:playlist_subgenre[T.classic rock] -1.3421 0.986 -1.361 0.173 -3.274 0.590
artist_n_tracks:playlist_subgenre[T.dance pop] 3.3154 0.936 3.541 0.000 1.480 5.151
artist_n_tracks:playlist_subgenre[T.electro house] 0.2556 0.870 0.294 0.769 -1.449 1.960
artist_n_tracks:playlist_subgenre[T.electropop] -2.1399 0.894 -2.393 0.017 -3.893 -0.387
artist_n_tracks:playlist_subgenre[T.gangster rap] -1.5403 0.880 -1.749 0.080 -3.266 0.185
artist_n_tracks:playlist_subgenre[T.hard rock] -0.8729 0.923 -0.946 0.344 -2.682 0.937
artist_n_tracks:playlist_subgenre[T.hip hop] 0.7471 0.911 0.820 0.412 -1.039 2.533
artist_n_tracks:playlist_subgenre[T.hip pop] -1.9162 1.119 -1.712 0.087 -4.110 0.278
artist_n_tracks:playlist_subgenre[T.indie poptimism] -0.2630 0.891 -0.295 0.768 -2.009 1.483
artist_n_tracks:playlist_subgenre[T.latin hip hop] -3.0028 0.889 -3.379 0.001 -4.744 -1.261
artist_n_tracks:playlist_subgenre[T.latin pop] -0.1056 0.924 -0.114 0.909 -1.916 1.705
artist_n_tracks:playlist_subgenre[T.neo soul] -1.5179 0.831 -1.826 0.068 -3.147 0.111
artist_n_tracks:playlist_subgenre[T.new jack swing] -1.8331 1.027 -1.785 0.074 -3.846 0.179
artist_n_tracks:playlist_subgenre[T.permanent wave] 1.4990 0.965 1.553 0.120 -0.393 3.390
artist_n_tracks:playlist_subgenre[T.pop edm] -2.0537 0.981 -2.093 0.036 -3.977 -0.131
artist_n_tracks:playlist_subgenre[T.post-teen pop] 1.0652 1.033 1.031 0.303 -0.960 3.091
artist_n_tracks:playlist_subgenre[T.progressive electro house] -2.7579 0.839 -3.288 0.001 -4.402 -1.114
artist_n_tracks:playlist_subgenre[T.reggaeton] 1.9324 1.146 1.686 0.092 -0.315 4.179
artist_n_tracks:playlist_subgenre[T.southern hip hop] -0.0374 0.839 -0.045 0.964 -1.681 1.606
artist_n_tracks:playlist_subgenre[T.trap] -0.3231 0.955 -0.338 0.735 -2.195 1.549
artist_n_tracks:playlist_subgenre[T.tropical] -1.1237 0.970 -1.159 0.247 -3.024 0.777
artist_n_tracks:playlist_subgenre[T.urban contemporary] 1.7128 0.895 1.914 0.056 -0.041 3.467
I(artist_avg_popularity ** 2) 3.0143 0.313 9.635 0.000 2.401 3.627
I(artist_avg_popularity ** 2):playlist_subgenre[T.big room] 0.6817 0.479 1.422 0.155 -0.258 1.621
I(artist_avg_popularity ** 2):playlist_subgenre[T.classic rock] 0.6366 0.478 1.330 0.183 -0.301 1.575
I(artist_avg_popularity ** 2):playlist_subgenre[T.dance pop] 0.6401 0.622 1.028 0.304 -0.580 1.860
I(artist_avg_popularity ** 2):playlist_subgenre[T.electro house] 0.7843 0.442 1.774 0.076 -0.082 1.651
I(artist_avg_popularity ** 2):playlist_subgenre[T.electropop] 1.0065 0.420 2.399 0.016 0.184 1.829
I(artist_avg_popularity ** 2):playlist_subgenre[T.gangster rap] 1.2797 0.420 3.044 0.002 0.456 2.104
I(artist_avg_popularity ** 2):playlist_subgenre[T.hard rock] 1.9650 0.454 4.329 0.000 1.075 2.855
I(artist_avg_popularity ** 2):playlist_subgenre[T.hip hop] 0.8391 0.809 1.037 0.300 -0.746 2.425
I(artist_avg_popularity ** 2):playlist_subgenre[T.hip pop] 0.8694 0.496 1.753 0.080 -0.103 1.842
I(artist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism] 1.1244 0.414 2.716 0.007 0.313 1.936
I(artist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop] 0.5825 0.406 1.433 0.152 -0.214 1.379
I(artist_avg_popularity ** 2):playlist_subgenre[T.latin pop] 1.5068 0.481 3.130 0.002 0.563 2.451
I(artist_avg_popularity ** 2):playlist_subgenre[T.neo soul] 0.6816 0.393 1.736 0.083 -0.088 1.451
I(artist_avg_popularity ** 2):playlist_subgenre[T.new jack swing] 0.5731 0.501 1.143 0.253 -0.409 1.556
I(artist_avg_popularity ** 2):playlist_subgenre[T.permanent wave] 0.6519 0.685 0.951 0.341 -0.691 1.995
I(artist_avg_popularity ** 2):playlist_subgenre[T.pop edm] 1.1644 0.484 2.408 0.016 0.217 2.112
I(artist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop] 0.7841 0.532 1.474 0.140 -0.258 1.827
I(artist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house] -0.0892 0.395 -0.226 0.821 -0.864 0.685
I(artist_avg_popularity ** 2):playlist_subgenre[T.reggaeton] 1.4927 0.687 2.174 0.030 0.147 2.838
I(artist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop] 1.1265 0.422 2.669 0.008 0.299 1.954
I(artist_avg_popularity ** 2):playlist_subgenre[T.trap] 1.4812 0.554 2.676 0.007 0.396 2.566
I(artist_avg_popularity ** 2):playlist_subgenre[T.tropical] 2.4073 0.602 4.001 0.000 1.228 3.587
I(artist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary] 0.9372 0.445 2.107 0.035 0.066 1.809
I(playlist_avg_popularity ** 2) 2.1446 0.198 10.819 0.000 1.756 2.533
I(playlist_avg_popularity ** 2):playlist_subgenre[T.big room] -1.5693 0.642 -2.445 0.014 -2.827 -0.311
I(playlist_avg_popularity ** 2):playlist_subgenre[T.classic rock] 5.1724 1.149 4.501 0.000 2.920 7.425
I(playlist_avg_popularity ** 2):playlist_subgenre[T.dance pop] 4.4731 1.703 2.627 0.009 1.135 7.811
I(playlist_avg_popularity ** 2):playlist_subgenre[T.electro house] -1.9415 0.621 -3.127 0.002 -3.158 -0.725
I(playlist_avg_popularity ** 2):playlist_subgenre[T.electropop] 1.5226 0.375 4.058 0.000 0.787 2.258
I(playlist_avg_popularity ** 2):playlist_subgenre[T.gangster rap] 0.0970 0.795 0.122 0.903 -1.462 1.656
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hard rock] -1.6179 0.406 -3.982 0.000 -2.414 -0.822
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip hop] 1.9823 2.647 0.749 0.454 -3.206 7.170
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip pop] 1.1151 1.087 1.026 0.305 -1.015 3.245
I(playlist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism] 0.5326 0.749 0.711 0.477 -0.936 2.001
I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop] -1.0956 0.264 -4.151 0.000 -1.613 -0.578
I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin pop] 1.4728 1.078 1.366 0.172 -0.640 3.586
I(playlist_avg_popularity ** 2):playlist_subgenre[T.neo soul] -0.4169 0.299 -1.396 0.163 -1.002 0.169
I(playlist_avg_popularity ** 2):playlist_subgenre[T.new jack swing] 0.1140 1.115 0.102 0.919 -2.071 2.299
I(playlist_avg_popularity ** 2):playlist_subgenre[T.permanent wave] 3.0497 2.077 1.469 0.142 -1.021 7.120
I(playlist_avg_popularity ** 2):playlist_subgenre[T.pop edm] 0.6878 0.746 0.921 0.357 -0.775 2.151
I(playlist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop] 2.3608 0.700 3.374 0.001 0.989 3.732
I(playlist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house] -0.8737 0.391 -2.236 0.025 -1.639 -0.108
I(playlist_avg_popularity ** 2):playlist_subgenre[T.reggaeton] -1.3945 1.200 -1.162 0.245 -3.747 0.958
I(playlist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop] 3.1843 0.879 3.622 0.000 1.461 4.907
I(playlist_avg_popularity ** 2):playlist_subgenre[T.trap] -0.0560 1.907 -0.029 0.977 -3.794 3.682
I(playlist_avg_popularity ** 2):playlist_subgenre[T.tropical] -4.4527 2.271 -1.960 0.050 -8.905 -0.001
I(playlist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary] 1.0602 0.835 1.269 0.204 -0.577 2.698
I(danceability ** 2) 0.2649 0.323 0.819 0.413 -0.369 0.898
I(danceability ** 2):playlist_subgenre[T.big room] 0.1994 0.539 0.370 0.711 -0.857 1.256
I(danceability ** 2):playlist_subgenre[T.classic rock] 0.2881 0.463 0.623 0.533 -0.618 1.195
I(danceability ** 2):playlist_subgenre[T.dance pop] 0.5113 0.548 0.934 0.350 -0.562 1.585
I(danceability ** 2):playlist_subgenre[T.electro house] -0.0877 0.549 -0.160 0.873 -1.165 0.989
I(danceability ** 2):playlist_subgenre[T.electropop] -0.0362 0.480 -0.075 0.940 -0.977 0.905
I(danceability ** 2):playlist_subgenre[T.gangster rap] -0.2427 0.548 -0.442 0.658 -1.318 0.832
I(danceability ** 2):playlist_subgenre[T.hard rock] 0.6863 0.497 1.381 0.167 -0.287 1.660
I(danceability ** 2):playlist_subgenre[T.hip hop] 0.0414 0.522 0.079 0.937 -0.981 1.064
I(danceability ** 2):playlist_subgenre[T.hip pop] -0.0449 0.575 -0.078 0.938 -1.172 1.082
I(danceability ** 2):playlist_subgenre[T.indie poptimism] -0.6390 0.451 -1.418 0.156 -1.522 0.244
I(danceability ** 2):playlist_subgenre[T.latin hip hop] 0.3075 0.641 0.480 0.631 -0.948 1.563
I(danceability ** 2):playlist_subgenre[T.latin pop] -0.1345 0.507 -0.265 0.791 -1.127 0.858
I(danceability ** 2):playlist_subgenre[T.neo soul] -0.9196 0.463 -1.986 0.047 -1.827 -0.012
I(danceability ** 2):playlist_subgenre[T.new jack swing] -0.4956 0.704 -0.705 0.481 -1.875 0.883
I(danceability ** 2):playlist_subgenre[T.permanent wave] -0.2190 0.480 -0.457 0.648 -1.159 0.721
I(danceability ** 2):playlist_subgenre[T.pop edm] -0.0068 0.584 -0.012 0.991 -1.151 1.138
I(danceability ** 2):playlist_subgenre[T.post-teen pop] 0.3897 0.509 0.766 0.444 -0.608 1.387
I(danceability ** 2):playlist_subgenre[T.progressive electro house] -0.0953 0.532 -0.179 0.858 -1.137 0.947
I(danceability ** 2):playlist_subgenre[T.reggaeton] 0.3314 1.049 0.316 0.752 -1.725 2.388
I(danceability ** 2):playlist_subgenre[T.southern hip hop] 0.1014 0.427 0.237 0.813 -0.736 0.939
I(danceability ** 2):playlist_subgenre[T.trap] 0.1847 0.515 0.359 0.720 -0.825 1.194
I(danceability ** 2):playlist_subgenre[T.tropical] -0.0990 0.461 -0.215 0.830 -1.002 0.804
I(danceability ** 2):playlist_subgenre[T.urban contemporary] -0.0852 0.437 -0.195 0.845 -0.941 0.771
I(energy ** 2) -0.0175 0.293 -0.060 0.952 -0.592 0.557
I(energy ** 2):playlist_subgenre[T.big room] -1.4620 0.889 -1.645 0.100 -3.204 0.280
I(energy ** 2):playlist_subgenre[T.classic rock] -0.6209 0.489 -1.271 0.204 -1.578 0.337
I(energy ** 2):playlist_subgenre[T.dance pop] -0.7165 0.497 -1.443 0.149 -1.690 0.257
I(energy ** 2):playlist_subgenre[T.electro house] -0.2810 0.550 -0.511 0.610 -1.360 0.798
I(energy ** 2):playlist_subgenre[T.electropop] -0.0698 0.481 -0.145 0.885 -1.013 0.873
I(energy ** 2):playlist_subgenre[T.gangster rap] -0.2307 0.580 -0.398 0.691 -1.367 0.905
I(energy ** 2):playlist_subgenre[T.hard rock] -0.4410 0.567 -0.778 0.436 -1.551 0.669
I(energy ** 2):playlist_subgenre[T.hip hop] 0.0625 0.389 0.161 0.872 -0.700 0.825
I(energy ** 2):playlist_subgenre[T.hip pop] 0.3128 0.536 0.584 0.560 -0.738 1.364
I(energy ** 2):playlist_subgenre[T.indie poptimism] -0.1241 0.402 -0.309 0.758 -0.912 0.664
I(energy ** 2):playlist_subgenre[T.latin hip hop] 0.3285 0.628 0.523 0.601 -0.903 1.560
I(energy ** 2):playlist_subgenre[T.latin pop] -0.0364 0.474 -0.077 0.939 -0.966 0.893
I(energy ** 2):playlist_subgenre[T.neo soul] -0.0741 0.408 -0.181 0.856 -0.874 0.726
I(energy ** 2):playlist_subgenre[T.new jack swing] -1.3440 0.546 -2.461 0.014 -2.414 -0.274
I(energy ** 2):playlist_subgenre[T.permanent wave] 0.3975 0.433 0.918 0.358 -0.451 1.246
I(energy ** 2):playlist_subgenre[T.pop edm] 0.7498 0.722 1.039 0.299 -0.665 2.165
I(energy ** 2):playlist_subgenre[T.post-teen pop] -0.3882 0.523 -0.743 0.458 -1.412 0.636
I(energy ** 2):playlist_subgenre[T.progressive electro house] -0.2373 0.707 -0.336 0.737 -1.623 1.148
I(energy ** 2):playlist_subgenre[T.reggaeton] -2.2161 1.282 -1.729 0.084 -4.728 0.296
I(energy ** 2):playlist_subgenre[T.southern hip hop] -0.9652 0.550 -1.755 0.079 -2.043 0.113
I(energy ** 2):playlist_subgenre[T.trap] -0.0792 0.548 -0.144 0.885 -1.153 0.995
I(energy ** 2):playlist_subgenre[T.tropical] 0.0057 0.475 0.012 0.990 -0.926 0.937
I(energy ** 2):playlist_subgenre[T.urban contemporary] -0.3312 0.405 -0.818 0.414 -1.125 0.463
I(valence ** 2) -0.5836 0.439 -1.328 0.184 -1.445 0.278
I(valence ** 2):playlist_subgenre[T.big room] 0.6043 0.694 0.870 0.384 -0.757 1.965
I(valence ** 2):playlist_subgenre[T.classic rock] 0.7081 0.668 1.060 0.289 -0.601 2.017
I(valence ** 2):playlist_subgenre[T.dance pop] 0.9086 0.628 1.446 0.148 -0.323 2.140
I(valence ** 2):playlist_subgenre[T.electro house] 0.9082 0.565 1.606 0.108 -0.200 2.017
I(valence ** 2):playlist_subgenre[T.electropop] 0.2253 0.606 0.372 0.710 -0.962 1.413
I(valence ** 2):playlist_subgenre[T.gangster rap] 0.0025 0.582 0.004 0.997 -1.138 1.144
I(valence ** 2):playlist_subgenre[T.hard rock] -0.6834 0.685 -0.998 0.318 -2.025 0.658
I(valence ** 2):playlist_subgenre[T.hip hop] 0.7829 0.600 1.305 0.192 -0.393 1.959
I(valence ** 2):playlist_subgenre[T.hip pop] 0.6640 0.700 0.948 0.343 -0.708 2.036
I(valence ** 2):playlist_subgenre[T.indie poptimism] 0.4039 0.577 0.700 0.484 -0.727 1.535
I(valence ** 2):playlist_subgenre[T.latin hip hop] 0.8305 0.649 1.280 0.200 -0.441 2.102
I(valence ** 2):playlist_subgenre[T.latin pop] 0.5437 0.665 0.818 0.413 -0.759 1.847
I(valence ** 2):playlist_subgenre[T.neo soul] 0.8787 0.621 1.415 0.157 -0.339 2.096
I(valence ** 2):playlist_subgenre[T.new jack swing] 0.8117 0.764 1.063 0.288 -0.685 2.308
I(valence ** 2):playlist_subgenre[T.permanent wave] 0.6438 0.654 0.985 0.325 -0.637 1.925
I(valence ** 2):playlist_subgenre[T.pop edm] 0.6054 0.674 0.899 0.369 -0.715 1.926
I(valence ** 2):playlist_subgenre[T.post-teen pop] 1.1934 0.699 1.707 0.088 -0.177 2.563
I(valence ** 2):playlist_subgenre[T.progressive electro house] 0.6819 0.564 1.210 0.226 -0.423 1.787
I(valence ** 2):playlist_subgenre[T.reggaeton] 0.0714 0.933 0.077 0.939 -1.758 1.901
I(valence ** 2):playlist_subgenre[T.southern hip hop] 1.0214 0.604 1.692 0.091 -0.162 2.204
I(valence ** 2):playlist_subgenre[T.trap] 1.2265 0.622 1.972 0.049 0.007 2.446
I(valence ** 2):playlist_subgenre[T.tropical] 0.3562 0.620 0.574 0.566 -0.860 1.572
I(valence ** 2):playlist_subgenre[T.urban contemporary] 1.1186 0.607 1.842 0.066 -0.072 2.309
I(tempo ** 2) 0.0550 0.094 0.585 0.558 -0.129 0.239
I(tempo ** 2):playlist_subgenre[T.big room] -0.8050 0.728 -1.106 0.269 -2.232 0.622
I(tempo ** 2):playlist_subgenre[T.classic rock] -0.6458 0.395 -1.634 0.102 -1.420 0.129
I(tempo ** 2):playlist_subgenre[T.dance pop] -0.0482 0.419 -0.115 0.908 -0.870 0.773
I(tempo ** 2):playlist_subgenre[T.electro house] -0.2538 0.666 -0.381 0.703 -1.559 1.052
I(tempo ** 2):playlist_subgenre[T.electropop] -1.0798 0.439 -2.459 0.014 -1.940 -0.219
I(tempo ** 2):playlist_subgenre[T.gangster rap] -0.2450 0.367 -0.668 0.504 -0.964 0.474
I(tempo ** 2):playlist_subgenre[T.hard rock] -0.0993 0.387 -0.256 0.798 -0.858 0.659
I(tempo ** 2):playlist_subgenre[T.hip hop] 0.1026 0.312 0.329 0.742 -0.508 0.713
I(tempo ** 2):playlist_subgenre[T.hip pop] -0.3362 0.416 -0.809 0.419 -1.151 0.479
I(tempo ** 2):playlist_subgenre[T.indie poptimism] 0.1841 0.349 0.527 0.598 -0.500 0.868
I(tempo ** 2):playlist_subgenre[T.latin hip hop] -0.5719 0.390 -1.466 0.143 -1.336 0.193
I(tempo ** 2):playlist_subgenre[T.latin pop] 0.2194 0.408 0.537 0.591 -0.581 1.020
I(tempo ** 2):playlist_subgenre[T.neo soul] -0.3225 0.301 -1.070 0.284 -0.913 0.268
I(tempo ** 2):playlist_subgenre[T.new jack swing] 0.0637 0.403 0.158 0.874 -0.725 0.853
I(tempo ** 2):playlist_subgenre[T.permanent wave] 0.3241 0.365 0.889 0.374 -0.391 1.039
I(tempo ** 2):playlist_subgenre[T.pop edm] -0.8973 0.515 -1.742 0.082 -1.907 0.112
I(tempo ** 2):playlist_subgenre[T.post-teen pop] 0.6401 0.403 1.589 0.112 -0.150 1.430
I(tempo ** 2):playlist_subgenre[T.progressive electro house] 1.3411 0.828 1.619 0.105 -0.282 2.964
I(tempo ** 2):playlist_subgenre[T.reggaeton] -0.8134 0.610 -1.333 0.182 -2.009 0.382
I(tempo ** 2):playlist_subgenre[T.southern hip hop] -0.0441 0.324 -0.136 0.892 -0.679 0.591
I(tempo ** 2):playlist_subgenre[T.trap] 0.9511 0.444 2.142 0.032 0.081 1.822
I(tempo ** 2):playlist_subgenre[T.tropical] -0.1804 0.491 -0.367 0.714 -1.144 0.783
I(tempo ** 2):playlist_subgenre[T.urban contemporary] -0.1039 0.333 -0.312 0.755 -0.756 0.548
I(duration_ms ** 2) -0.0027 0.171 -0.016 0.987 -0.337 0.332
I(duration_ms ** 2):playlist_subgenre[T.big room] -0.3272 0.525 -0.623 0.533 -1.356 0.702
I(duration_ms ** 2):playlist_subgenre[T.classic rock] 0.0377 0.359 0.105 0.916 -0.666 0.742
I(duration_ms ** 2):playlist_subgenre[T.dance pop] 0.2462 0.451 0.546 0.585 -0.638 1.131
I(duration_ms ** 2):playlist_subgenre[T.electro house] 0.0293 0.202 0.145 0.884 -0.366 0.425
I(duration_ms ** 2):playlist_subgenre[T.electropop] -0.3959 0.350 -1.131 0.258 -1.082 0.290
I(duration_ms ** 2):playlist_subgenre[T.gangster rap] 0.1425 0.305 0.467 0.641 -0.456 0.741
I(duration_ms ** 2):playlist_subgenre[T.hard rock] -0.4932 0.402 -1.225 0.220 -1.282 0.296
I(duration_ms ** 2):playlist_subgenre[T.hip hop] 0.3407 0.262 1.303 0.193 -0.172 0.853
I(duration_ms ** 2):playlist_subgenre[T.hip pop] 0.0297 0.381 0.078 0.938 -0.718 0.777
I(duration_ms ** 2):playlist_subgenre[T.indie poptimism] 0.3458 0.541 0.639 0.523 -0.715 1.407
I(duration_ms ** 2):playlist_subgenre[T.latin hip hop] 0.2107 0.318 0.663 0.507 -0.412 0.834
I(duration_ms ** 2):playlist_subgenre[T.latin pop] -1.5357 0.447 -3.438 0.001 -2.411 -0.660
I(duration_ms ** 2):playlist_subgenre[T.neo soul] -0.1453 0.299 -0.486 0.627 -0.731 0.441
I(duration_ms ** 2):playlist_subgenre[T.new jack swing] 0.0824 0.299 0.275 0.783 -0.504 0.669
I(duration_ms ** 2):playlist_subgenre[T.permanent wave] 0.3317 0.421 0.788 0.430 -0.493 1.156
I(duration_ms ** 2):playlist_subgenre[T.pop edm] -0.4510 0.537 -0.840 0.401 -1.503 0.601
I(duration_ms ** 2):playlist_subgenre[T.post-teen pop] -0.3891 0.357 -1.091 0.275 -1.088 0.310
I(duration_ms ** 2):playlist_subgenre[T.progressive electro house] 0.4580 0.321 1.428 0.153 -0.171 1.086
I(duration_ms ** 2):playlist_subgenre[T.reggaeton] 0.3285 0.624 0.526 0.599 -0.895 1.552
I(duration_ms ** 2):playlist_subgenre[T.southern hip hop] 0.1558 0.239 0.653 0.514 -0.312 0.623
I(duration_ms ** 2):playlist_subgenre[T.trap] -0.3550 0.419 -0.848 0.397 -1.176 0.466
I(duration_ms ** 2):playlist_subgenre[T.tropical] -0.0558 0.299 -0.186 0.852 -0.643 0.531
I(duration_ms ** 2):playlist_subgenre[T.urban contemporary] -0.0390 0.312 -0.125 0.901 -0.651 0.573
I(artist_hit_rate ** 2) 0.9848 0.438 2.249 0.025 0.126 1.843
I(artist_hit_rate ** 2):playlist_subgenre[T.big room] 1.8300 1.342 1.364 0.173 -0.800 4.460
I(artist_hit_rate ** 2):playlist_subgenre[T.classic rock] -0.1991 0.634 -0.314 0.753 -1.441 1.043
I(artist_hit_rate ** 2):playlist_subgenre[T.dance pop] -0.7435 0.525 -1.417 0.156 -1.772 0.285
I(artist_hit_rate ** 2):playlist_subgenre[T.electro house] -0.5505 1.071 -0.514 0.607 -2.650 1.549
I(artist_hit_rate ** 2):playlist_subgenre[T.electropop] 0.0337 0.528 0.064 0.949 -1.002 1.069
I(artist_hit_rate ** 2):playlist_subgenre[T.gangster rap] 0.3181 0.583 0.546 0.585 -0.824 1.460
I(artist_hit_rate ** 2):playlist_subgenre[T.hard rock] 0.4292 0.663 0.647 0.518 -0.871 1.730
I(artist_hit_rate ** 2):playlist_subgenre[T.hip hop] -0.5786 0.510 -1.135 0.257 -1.578 0.421
I(artist_hit_rate ** 2):playlist_subgenre[T.hip pop] -1.4940 0.575 -2.597 0.009 -2.622 -0.366
I(artist_hit_rate ** 2):playlist_subgenre[T.indie poptimism] -0.2484 0.571 -0.435 0.664 -1.367 0.871
I(artist_hit_rate ** 2):playlist_subgenre[T.latin hip hop] -0.9207 0.581 -1.585 0.113 -2.059 0.218
I(artist_hit_rate ** 2):playlist_subgenre[T.latin pop] -0.9918 0.513 -1.934 0.053 -1.997 0.013
I(artist_hit_rate ** 2):playlist_subgenre[T.neo soul] 0.7899 0.661 1.194 0.232 -0.506 2.086
I(artist_hit_rate ** 2):playlist_subgenre[T.new jack swing] -0.3868 2.420 -0.160 0.873 -5.130 4.357
I(artist_hit_rate ** 2):playlist_subgenre[T.permanent wave] -1.0127 0.558 -1.814 0.070 -2.107 0.081
I(artist_hit_rate ** 2):playlist_subgenre[T.pop edm] 0.0581 0.601 0.097 0.923 -1.121 1.237
I(artist_hit_rate ** 2):playlist_subgenre[T.post-teen pop] -1.5462 0.538 -2.873 0.004 -2.601 -0.491
I(artist_hit_rate ** 2):playlist_subgenre[T.progressive electro house] -1.0285 1.160 -0.886 0.375 -3.303 1.246
I(artist_hit_rate ** 2):playlist_subgenre[T.reggaeton] 0.2030 0.586 0.346 0.729 -0.946 1.352
I(artist_hit_rate ** 2):playlist_subgenre[T.southern hip hop] -1.7004 0.693 -2.455 0.014 -3.058 -0.343
I(artist_hit_rate ** 2):playlist_subgenre[T.trap] 0.0034 0.563 0.006 0.995 -1.099 1.106
I(artist_hit_rate ** 2):playlist_subgenre[T.tropical] -0.0036 0.726 -0.005 0.996 -1.427 1.420
I(artist_hit_rate ** 2):playlist_subgenre[T.urban contemporary] -0.1060 0.521 -0.204 0.839 -1.127 0.915
I(artist_n_tracks ** 2) -0.6600 0.325 -2.028 0.043 -1.298 -0.022
I(artist_n_tracks ** 2):playlist_subgenre[T.big room] 0.4506 0.554 0.814 0.416 -0.635 1.536
I(artist_n_tracks ** 2):playlist_subgenre[T.classic rock] 0.7995 0.576 1.389 0.165 -0.329 1.928
I(artist_n_tracks ** 2):playlist_subgenre[T.dance pop] 0.6981 0.536 1.303 0.193 -0.352 1.748
I(artist_n_tracks ** 2):playlist_subgenre[T.electro house] 0.7114 0.520 1.369 0.171 -0.307 1.730
I(artist_n_tracks ** 2):playlist_subgenre[T.electropop] 1.7907 0.534 3.353 0.001 0.744 2.837
I(artist_n_tracks ** 2):playlist_subgenre[T.gangster rap] 0.8635 0.574 1.504 0.132 -0.261 1.988
I(artist_n_tracks ** 2):playlist_subgenre[T.hard rock] 0.3207 0.628 0.511 0.610 -0.910 1.552
I(artist_n_tracks ** 2):playlist_subgenre[T.hip hop] -0.4291 0.560 -0.766 0.444 -1.527 0.669
I(artist_n_tracks ** 2):playlist_subgenre[T.hip pop] -0.4483 0.808 -0.555 0.579 -2.032 1.135
I(artist_n_tracks ** 2):playlist_subgenre[T.indie poptimism] 1.1739 0.693 1.695 0.090 -0.184 2.532
I(artist_n_tracks ** 2):playlist_subgenre[T.latin hip hop] 1.1132 0.575 1.937 0.053 -0.013 2.240
I(artist_n_tracks ** 2):playlist_subgenre[T.latin pop] 2.3191 0.634 3.656 0.000 1.076 3.563
I(artist_n_tracks ** 2):playlist_subgenre[T.neo soul] -0.3795 0.718 -0.528 0.597 -1.787 1.028
I(artist_n_tracks ** 2):playlist_subgenre[T.new jack swing] 0.3191 0.770 0.414 0.679 -1.190 1.828
I(artist_n_tracks ** 2):playlist_subgenre[T.permanent wave] 1.1494 0.745 1.543 0.123 -0.310 2.609
I(artist_n_tracks ** 2):playlist_subgenre[T.pop edm] 2.1646 0.590 3.669 0.000 1.008 3.321
I(artist_n_tracks ** 2):playlist_subgenre[T.post-teen pop] -0.5837 0.672 -0.869 0.385 -1.900 0.733
I(artist_n_tracks ** 2):playlist_subgenre[T.progressive electro house] 1.1728 0.509 2.302 0.021 0.174 2.171
I(artist_n_tracks ** 2):playlist_subgenre[T.reggaeton] -0.4667 0.603 -0.774 0.439 -1.649 0.715
I(artist_n_tracks ** 2):playlist_subgenre[T.southern hip hop] -0.0208 0.552 -0.038 0.970 -1.103 1.061
I(artist_n_tracks ** 2):playlist_subgenre[T.trap] -0.1617 0.654 -0.247 0.805 -1.443 1.120
I(artist_n_tracks ** 2):playlist_subgenre[T.tropical] -1.1311 0.707 -1.599 0.110 -2.518 0.255
I(artist_n_tracks ** 2):playlist_subgenre[T.urban contemporary] -0.0611 0.591 -0.103 0.918 -1.219 1.097
==============================================================================
Omnibus: 2088.556 Durbin-Watson: 1.742
Prob(Omnibus): 0.000 Jarque-Bera (JB): 4311.685
Skew: -0.499 Prob(JB): 0.00
Kurtosis: 4.629 Cond. No. 403.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
How many coefficients were estimated?
m_7.params.size
456
m_7.params[m_7.pvalues < 0.05].size
94
m_7.params[m_7.pvalues < 0.05].sort_values(key=abs,ascending=False)
Intercept 36.264634
artist_avg_popularity 19.577285
playlist_avg_popularity:playlist_subgenre[T.dance pop] -10.052623
playlist_avg_popularity 9.834377
playlist_subgenre[T.trap] -8.431859
...
I(tempo ** 2):playlist_subgenre[T.trap] 0.951109
I(artist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary] 0.937206
I(danceability ** 2):playlist_subgenre[T.neo soul] -0.919639
I(playlist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house] -0.873681
I(artist_n_tracks ** 2) -0.659975
Length: 94, dtype: float64
m_7.params[m_7.pvalues < 0.05].sort_values(ascending=False)[1:3]
artist_avg_popularity 19.577285 playlist_avg_popularity 9.834377 dtype: float64
print(f'R squared: {m_7.rsquared}, RMSE: {m_7.mse_resid**0.5}')
R squared: 0.6239669509284791, RMSE: 14.650902453727106
viz_fitted_vs_actual(m_7.fittedvalues, spotify_model['track_popularity'], 'Polynomial Interaction Model')
There is clear improvement with Polynomial interaction model over the ones before. More points are getting closer to the redline which indciates better performance.
Extra interactiont terms and complexity between polynomial and categorical.¶
f_8 = "track_popularity ~ \
(artist_avg_popularity + playlist_avg_popularity + danceability + energy + valence + \
tempo + duration_ms + artist_hit_rate + artist_n_tracks)*playlist_subgenre + \
(I(artist_avg_popularity**2) + I(playlist_avg_popularity**2) + I(danceability**2) + I(energy**2) + \
I(valence**2) + I(tempo**2) + I(duration_ms**2) + \
I(artist_hit_rate**2) + I(artist_n_tracks**2))*playlist_subgenre + \
(I(artist_avg_popularity**3) + I(playlist_avg_popularity**3) + I(danceability**3) + I(energy**3) + \
I(valence**3) + I(tempo**3) + I(duration_ms**3) + \
I(artist_hit_rate**3) + I(artist_n_tracks**3))*playlist_subgenre + \
artist_avg_popularity*I(artist_avg_popularity**2)*playlist_subgenre + \
artist_avg_popularity*I(artist_avg_popularity**3)*playlist_subgenre + \
I(artist_avg_popularity**2)*I(artist_avg_popularity**3)*playlist_subgenre + \
playlist_avg_popularity*I(playlist_avg_popularity**2)*playlist_subgenre + \
playlist_avg_popularity*I(playlist_avg_popularity**3)*playlist_subgenre + \
I(playlist_avg_popularity**2)*I(playlist_avg_popularity**3)*playlist_subgenre + \
danceability*I(danceability**2)*playlist_subgenre + \
danceability*I(danceability**3)*playlist_subgenre + \
I(danceability**2)*I(danceability**3)*playlist_subgenre + \
energy*I(energy**2)*playlist_subgenre + \
energy*I(energy**3)*playlist_subgenre + \
I(energy**2)*I(energy**3)*playlist_subgenre + \
valence*I(valence**2)*playlist_subgenre + \
valence*I(valence**3)*playlist_subgenre + \
I(valence**2)*I(valence**3)*playlist_subgenre + \
tempo*I(tempo**2)*playlist_subgenre + \
tempo*I(tempo**3)*playlist_subgenre + \
I(tempo**2)*I(tempo**3)*playlist_subgenre + \
duration_ms*I(duration_ms**2)*playlist_subgenre + \
duration_ms*I(duration_ms**3)*playlist_subgenre + \
I(duration_ms**2)*I(duration_ms**3)*playlist_subgenre + \
artist_hit_rate*I(artist_hit_rate**2)*playlist_subgenre + \
artist_hit_rate*I(artist_hit_rate**3)*playlist_subgenre + \
I(artist_hit_rate**2)*I(artist_hit_rate**3)*playlist_subgenre + \
artist_n_tracks*I(artist_n_tracks**2)*playlist_subgenre + \
artist_n_tracks*I(artist_n_tracks**3)*playlist_subgenre + \
I(artist_n_tracks**2)*I(artist_n_tracks**3)*playlist_subgenre"
m_8 = fit_ols(f_8, spotify_model)
OLS Regression Results
==============================================================================
Dep. Variable: track_popularity R-squared: 0.640
Model: OLS Adj. R-squared: 0.626
Method: Least Squares F-statistic: 44.00
Date: Wed, 10 Dec 2025 Prob (F-statistic): 0.00
Time: 06:30:02 Log-Likelihood: -1.1548e+05
No. Observations: 28352 AIC: 2.332e+05
Df Residuals: 27248 BIC: 2.423e+05
Df Model: 1103
Covariance Type: nonrobust
==================================================================================================================================================================================
coef std err t P>|t| [0.025 0.975]
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Intercept 34.6557 2.522 13.742 0.000 29.713 39.599
playlist_subgenre[T.big room] -4.7624 3.971 -1.199 0.230 -12.546 3.022
playlist_subgenre[T.classic rock] -9.5650 3.418 -2.799 0.005 -16.264 -2.866
playlist_subgenre[T.dance pop] 7.7352 3.740 2.068 0.039 0.404 15.066
playlist_subgenre[T.electro house] 3.3298 4.160 0.800 0.423 -4.823 11.483
playlist_subgenre[T.electropop] -5.9354 3.400 -1.746 0.081 -12.599 0.729
playlist_subgenre[T.gangster rap] -4.9753 3.480 -1.430 0.153 -11.797 1.846
playlist_subgenre[T.hard rock] -0.3161 3.567 -0.089 0.929 -7.308 6.676
playlist_subgenre[T.hip hop] 36.5264 21.712 1.682 0.093 -6.031 79.084
playlist_subgenre[T.hip pop] -9.6941 4.979 -1.947 0.052 -19.453 0.065
playlist_subgenre[T.indie poptimism] -5.7996 3.472 -1.670 0.095 -12.605 1.005
playlist_subgenre[T.latin hip hop] -7.6260 3.686 -2.069 0.039 -14.852 -0.400
playlist_subgenre[T.latin pop] -7.5552 3.668 -2.060 0.039 -14.745 -0.366
playlist_subgenre[T.neo soul] -6.7755 3.478 -1.948 0.051 -13.593 0.042
playlist_subgenre[T.new jack swing] -4.5803 4.049 -1.131 0.258 -12.516 3.355
playlist_subgenre[T.permanent wave] 8.0959 3.997 2.025 0.043 0.261 15.931
playlist_subgenre[T.pop edm] -6.6616 3.872 -1.721 0.085 -14.250 0.927
playlist_subgenre[T.post-teen pop] -3.2652 3.810 -0.857 0.391 -10.733 4.203
playlist_subgenre[T.progressive electro house] -5.2927 3.595 -1.472 0.141 -12.340 1.754
playlist_subgenre[T.reggaeton] -5.2798 4.920 -1.073 0.283 -14.924 4.364
playlist_subgenre[T.southern hip hop] 0.1906 3.280 0.058 0.954 -6.238 6.619
playlist_subgenre[T.trap] -6.4616 3.697 -1.748 0.080 -13.707 0.784
playlist_subgenre[T.tropical] -3.7755 3.903 -0.967 0.333 -11.426 3.875
playlist_subgenre[T.urban contemporary] -1.6477 4.033 -0.409 0.683 -9.553 6.258
artist_avg_popularity 16.5742 2.229 7.437 0.000 12.206 20.943
artist_avg_popularity:playlist_subgenre[T.big room] 5.7074 2.966 1.924 0.054 -0.107 11.522
artist_avg_popularity:playlist_subgenre[T.classic rock] 0.5545 3.077 0.180 0.857 -5.476 6.585
artist_avg_popularity:playlist_subgenre[T.dance pop] 3.2800 3.106 1.056 0.291 -2.808 9.368
artist_avg_popularity:playlist_subgenre[T.electro house] 5.7114 2.934 1.947 0.052 -0.040 11.463
artist_avg_popularity:playlist_subgenre[T.electropop] 4.8313 2.945 1.640 0.101 -0.941 10.604
artist_avg_popularity:playlist_subgenre[T.gangster rap] 8.6288 2.841 3.037 0.002 3.061 14.197
artist_avg_popularity:playlist_subgenre[T.hard rock] 8.5290 2.907 2.934 0.003 2.831 14.227
artist_avg_popularity:playlist_subgenre[T.hip hop] -0.8150 3.320 -0.245 0.806 -7.323 5.693
artist_avg_popularity:playlist_subgenre[T.hip pop] 7.1454 3.362 2.126 0.034 0.556 13.734
artist_avg_popularity:playlist_subgenre[T.indie poptimism] 6.6342 2.793 2.376 0.018 1.161 12.108
artist_avg_popularity:playlist_subgenre[T.latin hip hop] 8.8040 2.959 2.976 0.003 3.005 14.603
artist_avg_popularity:playlist_subgenre[T.latin pop] 10.5595 3.198 3.302 0.001 4.292 16.827
artist_avg_popularity:playlist_subgenre[T.neo soul] 6.2063 2.683 2.313 0.021 0.948 11.465
artist_avg_popularity:playlist_subgenre[T.new jack swing] 8.4474 2.975 2.840 0.005 2.617 14.278
artist_avg_popularity:playlist_subgenre[T.permanent wave] 8.7205 3.171 2.750 0.006 2.505 14.936
artist_avg_popularity:playlist_subgenre[T.pop edm] 5.8808 3.165 1.858 0.063 -0.323 12.085
artist_avg_popularity:playlist_subgenre[T.post-teen pop] 8.7436 3.291 2.657 0.008 2.293 15.194
artist_avg_popularity:playlist_subgenre[T.progressive electro house] 3.8907 2.710 1.436 0.151 -1.421 9.202
artist_avg_popularity:playlist_subgenre[T.reggaeton] 1.0426 3.901 0.267 0.789 -6.604 8.689
artist_avg_popularity:playlist_subgenre[T.southern hip hop] 7.0990 2.765 2.568 0.010 1.680 12.518
artist_avg_popularity:playlist_subgenre[T.trap] 4.0024 3.369 1.188 0.235 -2.600 10.605
artist_avg_popularity:playlist_subgenre[T.tropical] 9.0590 3.015 3.005 0.003 3.149 14.969
artist_avg_popularity:playlist_subgenre[T.urban contemporary] 3.2027 3.026 1.059 0.290 -2.728 9.133
playlist_avg_popularity 7.8082 1.720 4.541 0.000 4.438 11.179
playlist_avg_popularity:playlist_subgenre[T.big room] -8.9086 4.734 -1.882 0.060 -18.187 0.370
playlist_avg_popularity:playlist_subgenre[T.classic rock] 7.1008 3.331 2.132 0.033 0.572 13.630
playlist_avg_popularity:playlist_subgenre[T.dance pop] -3.4008 5.072 -0.670 0.503 -13.343 6.541
playlist_avg_popularity:playlist_subgenre[T.electro house] -2.3276 3.172 -0.734 0.463 -8.544 3.889
playlist_avg_popularity:playlist_subgenre[T.electropop] -4.1414 2.427 -1.707 0.088 -8.898 0.615
playlist_avg_popularity:playlist_subgenre[T.gangster rap] -2.6495 2.625 -1.009 0.313 -7.795 2.496
playlist_avg_popularity:playlist_subgenre[T.hard rock] -0.4248 2.702 -0.157 0.875 -5.721 4.871
playlist_avg_popularity:playlist_subgenre[T.hip hop] -300.9947 160.470 -1.876 0.061 -615.524 13.535
playlist_avg_popularity:playlist_subgenre[T.hip pop] -2.6363 5.797 -0.455 0.649 -13.998 8.725
playlist_avg_popularity:playlist_subgenre[T.indie poptimism] 0.8728 3.237 0.270 0.787 -5.473 7.218
playlist_avg_popularity:playlist_subgenre[T.latin hip hop] -2.8859 2.280 -1.266 0.206 -7.355 1.583
playlist_avg_popularity:playlist_subgenre[T.latin pop] -7.9874 4.062 -1.967 0.049 -15.948 -0.026
playlist_avg_popularity:playlist_subgenre[T.neo soul] -2.3801 2.571 -0.926 0.355 -7.419 2.659
playlist_avg_popularity:playlist_subgenre[T.new jack swing] -1.8235 5.109 -0.357 0.721 -11.837 8.190
playlist_avg_popularity:playlist_subgenre[T.permanent wave] -14.4854 8.821 -1.642 0.101 -31.776 2.805
playlist_avg_popularity:playlist_subgenre[T.pop edm] -0.5312 3.324 -0.160 0.873 -7.046 5.983
playlist_avg_popularity:playlist_subgenre[T.post-teen pop] 40.5455 14.992 2.704 0.007 11.159 69.931
playlist_avg_popularity:playlist_subgenre[T.progressive electro house] 5.1345 2.684 1.913 0.056 -0.126 10.395
playlist_avg_popularity:playlist_subgenre[T.reggaeton] 8.6449 4.797 1.802 0.072 -0.758 18.048
playlist_avg_popularity:playlist_subgenre[T.southern hip hop] 3.8803 2.798 1.387 0.166 -1.604 9.364
playlist_avg_popularity:playlist_subgenre[T.trap] -1.3598 7.458 -0.182 0.855 -15.979 13.259
playlist_avg_popularity:playlist_subgenre[T.tropical] -12.1565 5.276 -2.304 0.021 -22.498 -1.815
playlist_avg_popularity:playlist_subgenre[T.urban contemporary] -7.7584 3.712 -2.090 0.037 -15.034 -0.483
danceability 1.5729 1.556 1.011 0.312 -1.478 4.624
danceability:playlist_subgenre[T.big room] -1.7488 2.011 -0.870 0.384 -5.690 2.192
danceability:playlist_subgenre[T.classic rock] -0.1768 2.072 -0.085 0.932 -4.239 3.885
danceability:playlist_subgenre[T.dance pop] -1.2252 1.933 -0.634 0.526 -5.014 2.564
danceability:playlist_subgenre[T.electro house] -2.1256 2.046 -1.039 0.299 -6.137 1.886
danceability:playlist_subgenre[T.electropop] -0.0008 1.884 -0.000 1.000 -3.693 3.692
danceability:playlist_subgenre[T.gangster rap] -3.9531 2.055 -1.924 0.054 -7.980 0.074
danceability:playlist_subgenre[T.hard rock] 1.8868 2.587 0.729 0.466 -3.183 6.957
danceability:playlist_subgenre[T.hip hop] 0.4338 1.969 0.220 0.826 -3.425 4.293
danceability:playlist_subgenre[T.hip pop] -1.3467 2.080 -0.648 0.517 -5.423 2.730
danceability:playlist_subgenre[T.indie poptimism] -2.9556 1.835 -1.610 0.107 -6.553 0.642
danceability:playlist_subgenre[T.latin hip hop] 0.0588 2.224 0.026 0.979 -4.301 4.418
danceability:playlist_subgenre[T.latin pop] 1.0205 2.053 0.497 0.619 -3.004 5.045
danceability:playlist_subgenre[T.neo soul] -1.3200 1.813 -0.728 0.466 -4.873 2.233
danceability:playlist_subgenre[T.new jack swing] -4.0266 2.544 -1.583 0.113 -9.013 0.960
danceability:playlist_subgenre[T.permanent wave] -1.9878 2.187 -0.909 0.363 -6.274 2.298
danceability:playlist_subgenre[T.pop edm] -2.5646 1.991 -1.288 0.198 -6.467 1.338
danceability:playlist_subgenre[T.post-teen pop] 1.0596 1.971 0.538 0.591 -2.803 4.922
danceability:playlist_subgenre[T.progressive electro house] -0.8632 1.934 -0.446 0.655 -4.653 2.927
danceability:playlist_subgenre[T.reggaeton] -4.2456 3.294 -1.289 0.198 -10.703 2.212
danceability:playlist_subgenre[T.southern hip hop] -1.9929 1.794 -1.111 0.267 -5.510 1.524
danceability:playlist_subgenre[T.trap] -2.8977 2.026 -1.430 0.153 -6.869 1.073
danceability:playlist_subgenre[T.tropical] -0.9115 1.979 -0.461 0.645 -4.790 2.967
danceability:playlist_subgenre[T.urban contemporary] -0.7564 1.848 -0.409 0.682 -4.378 2.865
energy -1.2333 1.294 -0.953 0.341 -3.770 1.303
energy:playlist_subgenre[T.big room] 0.4963 3.334 0.149 0.882 -6.038 7.031
energy:playlist_subgenre[T.classic rock] -1.0395 1.779 -0.584 0.559 -4.526 2.447
energy:playlist_subgenre[T.dance pop] 0.4751 1.752 0.271 0.786 -2.958 3.909
energy:playlist_subgenre[T.electro house] 1.4172 1.785 0.794 0.427 -2.082 4.916
energy:playlist_subgenre[T.electropop] 3.0472 1.735 1.756 0.079 -0.353 6.448
energy:playlist_subgenre[T.gangster rap] 1.5859 1.783 0.889 0.374 -1.910 5.082
energy:playlist_subgenre[T.hard rock] 0.4531 1.988 0.228 0.820 -3.444 4.351
energy:playlist_subgenre[T.hip hop] 0.4607 1.872 0.246 0.806 -3.209 4.131
energy:playlist_subgenre[T.hip pop] 2.2222 2.140 1.038 0.299 -1.972 6.417
energy:playlist_subgenre[T.indie poptimism] -1.6401 1.753 -0.936 0.349 -5.076 1.795
energy:playlist_subgenre[T.latin hip hop] 2.4768 1.779 1.393 0.164 -1.009 5.963
energy:playlist_subgenre[T.latin pop] -0.4917 1.868 -0.263 0.792 -4.153 3.170
energy:playlist_subgenre[T.neo soul] -0.6746 1.851 -0.365 0.715 -4.302 2.953
energy:playlist_subgenre[T.new jack swing] 0.9488 1.854 0.512 0.609 -2.684 4.582
energy:playlist_subgenre[T.permanent wave] 1.2495 1.864 0.670 0.503 -2.403 4.902
energy:playlist_subgenre[T.pop edm] 1.9153 2.007 0.955 0.340 -2.018 5.848
energy:playlist_subgenre[T.post-teen pop] 0.7337 1.854 0.396 0.692 -2.899 4.367
energy:playlist_subgenre[T.progressive electro house] 2.4263 2.299 1.055 0.291 -2.079 6.932
energy:playlist_subgenre[T.reggaeton] -2.6866 3.094 -0.868 0.385 -8.750 3.377
energy:playlist_subgenre[T.southern hip hop] 0.6185 1.702 0.363 0.716 -2.717 3.954
energy:playlist_subgenre[T.trap] 3.6304 1.801 2.016 0.044 0.101 7.160
energy:playlist_subgenre[T.tropical] 0.2173 1.790 0.121 0.903 -3.291 3.726
energy:playlist_subgenre[T.urban contemporary] -0.3950 1.940 -0.204 0.839 -4.197 3.407
valence 0.8713 1.631 0.534 0.593 -2.325 4.067
valence:playlist_subgenre[T.big room] -3.5346 2.369 -1.492 0.136 -8.178 1.109
valence:playlist_subgenre[T.classic rock] -0.7646 2.407 -0.318 0.751 -5.482 3.953
valence:playlist_subgenre[T.dance pop] 1.6536 2.147 0.770 0.441 -2.554 5.861
valence:playlist_subgenre[T.electro house] 0.8359 2.067 0.404 0.686 -3.216 4.888
valence:playlist_subgenre[T.electropop] -1.1062 2.161 -0.512 0.609 -5.342 3.130
valence:playlist_subgenre[T.gangster rap] -0.6984 2.131 -0.328 0.743 -4.876 3.479
valence:playlist_subgenre[T.hard rock] -2.9810 2.210 -1.349 0.177 -7.312 1.350
valence:playlist_subgenre[T.hip hop] -4.3700 2.154 -2.029 0.043 -8.592 -0.148
valence:playlist_subgenre[T.hip pop] -1.7341 2.440 -0.711 0.477 -6.516 3.048
valence:playlist_subgenre[T.indie poptimism] -2.1703 2.044 -1.062 0.288 -6.177 1.837
valence:playlist_subgenre[T.latin hip hop] -1.6426 2.352 -0.699 0.485 -6.252 2.967
valence:playlist_subgenre[T.latin pop] -1.9653 2.459 -0.799 0.424 -6.785 2.854
valence:playlist_subgenre[T.neo soul] 0.7242 2.110 0.343 0.731 -3.411 4.860
valence:playlist_subgenre[T.new jack swing] -4.6102 2.660 -1.733 0.083 -9.823 0.603
valence:playlist_subgenre[T.permanent wave] -1.3050 2.364 -0.552 0.581 -5.938 3.328
valence:playlist_subgenre[T.pop edm] -2.9871 2.268 -1.317 0.188 -7.433 1.459
valence:playlist_subgenre[T.post-teen pop] -1.0227 2.376 -0.430 0.667 -5.680 3.635
valence:playlist_subgenre[T.progressive electro house] 0.0926 2.068 0.045 0.964 -3.961 4.147
valence:playlist_subgenre[T.reggaeton] 2.7934 3.267 0.855 0.393 -3.610 9.197
valence:playlist_subgenre[T.southern hip hop] -0.9877 2.109 -0.468 0.639 -5.121 3.145
valence:playlist_subgenre[T.trap] -2.5715 2.158 -1.192 0.233 -6.801 1.657
valence:playlist_subgenre[T.tropical] 3.0705 2.193 1.400 0.161 -1.227 7.368
valence:playlist_subgenre[T.urban contemporary] -1.0009 2.188 -0.458 0.647 -5.289 3.287
tempo -0.6311 0.854 -0.739 0.460 -2.305 1.043
tempo:playlist_subgenre[T.big room] 0.9117 2.933 0.311 0.756 -4.838 6.661
tempo:playlist_subgenre[T.classic rock] 1.3449 1.370 0.982 0.326 -1.340 4.030
tempo:playlist_subgenre[T.dance pop] 1.4217 1.409 1.009 0.313 -1.340 4.184
tempo:playlist_subgenre[T.electro house] 1.2181 2.193 0.555 0.579 -3.080 5.516
tempo:playlist_subgenre[T.electropop] 1.0378 1.487 0.698 0.485 -1.878 3.953
tempo:playlist_subgenre[T.gangster rap] 1.6847 1.308 1.288 0.198 -0.880 4.249
tempo:playlist_subgenre[T.hard rock] 2.3843 1.500 1.589 0.112 -0.556 5.325
tempo:playlist_subgenre[T.hip hop] 0.6379 1.128 0.566 0.572 -1.573 2.849
tempo:playlist_subgenre[T.hip pop] -0.9121 1.452 -0.628 0.530 -3.759 1.935
tempo:playlist_subgenre[T.indie poptimism] 1.9054 1.320 1.443 0.149 -0.683 4.494
tempo:playlist_subgenre[T.latin hip hop] 1.1509 1.421 0.810 0.418 -1.633 3.935
tempo:playlist_subgenre[T.latin pop] 1.4169 1.528 0.927 0.354 -1.579 4.412
tempo:playlist_subgenre[T.neo soul] 0.9190 1.182 0.778 0.437 -1.397 3.235
tempo:playlist_subgenre[T.new jack swing] -1.2659 1.824 -0.694 0.488 -4.842 2.310
tempo:playlist_subgenre[T.permanent wave] 0.7511 1.371 0.548 0.584 -1.936 3.438
tempo:playlist_subgenre[T.pop edm] 1.5442 1.648 0.937 0.349 -1.687 4.775
tempo:playlist_subgenre[T.post-teen pop] -0.2180 1.543 -0.141 0.888 -3.243 2.807
tempo:playlist_subgenre[T.progressive electro house] 2.2390 2.463 0.909 0.363 -2.588 7.066
tempo:playlist_subgenre[T.reggaeton] 4.7047 2.349 2.003 0.045 0.101 9.309
tempo:playlist_subgenre[T.southern hip hop] 0.2863 1.225 0.234 0.815 -2.114 2.687
tempo:playlist_subgenre[T.trap] -0.8195 1.667 -0.492 0.623 -4.087 2.448
tempo:playlist_subgenre[T.tropical] 2.3805 1.606 1.482 0.138 -0.767 5.528
tempo:playlist_subgenre[T.urban contemporary] 0.0919 1.385 0.066 0.947 -2.622 2.806
duration_ms -0.6693 0.874 -0.766 0.444 -2.382 1.044
duration_ms:playlist_subgenre[T.big room] 0.1305 1.809 0.072 0.943 -3.416 3.676
duration_ms:playlist_subgenre[T.classic rock] 0.6031 1.379 0.437 0.662 -2.099 3.305
duration_ms:playlist_subgenre[T.dance pop] 0.5880 1.553 0.379 0.705 -2.456 3.632
duration_ms:playlist_subgenre[T.electro house] -0.6474 1.082 -0.598 0.550 -2.769 1.474
duration_ms:playlist_subgenre[T.electropop] -1.3620 1.377 -0.989 0.323 -4.061 1.337
duration_ms:playlist_subgenre[T.gangster rap] 1.1770 1.231 0.956 0.339 -1.236 3.590
duration_ms:playlist_subgenre[T.hard rock] 0.7785 1.381 0.564 0.573 -1.929 3.486
duration_ms:playlist_subgenre[T.hip hop] 2.8626 1.298 2.205 0.027 0.318 5.407
duration_ms:playlist_subgenre[T.hip pop] 0.7141 1.397 0.511 0.609 -2.024 3.452
duration_ms:playlist_subgenre[T.indie poptimism] 1.8921 1.442 1.313 0.189 -0.933 4.718
duration_ms:playlist_subgenre[T.latin hip hop] 1.2790 1.256 1.018 0.309 -1.183 3.741
duration_ms:playlist_subgenre[T.latin pop] 0.4343 1.451 0.299 0.765 -2.409 3.277
duration_ms:playlist_subgenre[T.neo soul] 1.9046 1.224 1.556 0.120 -0.495 4.304
duration_ms:playlist_subgenre[T.new jack swing] 4.4554 1.990 2.238 0.025 0.554 8.357
duration_ms:playlist_subgenre[T.permanent wave] -0.1758 1.518 -0.116 0.908 -3.151 2.799
duration_ms:playlist_subgenre[T.pop edm] 0.4297 1.669 0.258 0.797 -2.841 3.701
duration_ms:playlist_subgenre[T.post-teen pop] 2.4348 1.489 1.635 0.102 -0.484 5.353
duration_ms:playlist_subgenre[T.progressive electro house] -1.0840 1.332 -0.814 0.416 -3.694 1.526
duration_ms:playlist_subgenre[T.reggaeton] 0.3219 1.786 0.180 0.857 -3.178 3.822
duration_ms:playlist_subgenre[T.southern hip hop] 1.8038 1.072 1.682 0.093 -0.298 3.906
duration_ms:playlist_subgenre[T.trap] -0.3950 1.457 -0.271 0.786 -3.250 2.460
duration_ms:playlist_subgenre[T.tropical] 0.9455 1.319 0.717 0.474 -1.641 3.532
duration_ms:playlist_subgenre[T.urban contemporary] 2.4620 1.268 1.942 0.052 -0.022 4.947
artist_hit_rate -2.8636 2.476 -1.156 0.248 -7.717 1.990
artist_hit_rate:playlist_subgenre[T.big room] -3.5974 6.731 -0.534 0.593 -16.791 9.596
artist_hit_rate:playlist_subgenre[T.classic rock] 5.9893 3.221 1.859 0.063 -0.324 12.303
artist_hit_rate:playlist_subgenre[T.dance pop] 2.2421 3.032 0.740 0.460 -3.700 8.184
artist_hit_rate:playlist_subgenre[T.electro house] -10.3121 5.468 -1.886 0.059 -21.030 0.406
artist_hit_rate:playlist_subgenre[T.electropop] -3.5969 2.992 -1.202 0.229 -9.461 2.268
artist_hit_rate:playlist_subgenre[T.gangster rap] -1.7299 3.152 -0.549 0.583 -7.907 4.447
artist_hit_rate:playlist_subgenre[T.hard rock] -2.7110 3.322 -0.816 0.414 -9.223 3.801
artist_hit_rate:playlist_subgenre[T.hip hop] 4.3098 3.181 1.355 0.175 -1.925 10.545
artist_hit_rate:playlist_subgenre[T.hip pop] 5.1269 3.606 1.422 0.155 -1.941 12.195
artist_hit_rate:playlist_subgenre[T.indie poptimism] 4.3791 3.097 1.414 0.157 -1.691 10.449
artist_hit_rate:playlist_subgenre[T.latin hip hop] 0.4215 3.154 0.134 0.894 -5.761 6.604
artist_hit_rate:playlist_subgenre[T.latin pop] 2.6037 3.040 0.856 0.392 -3.355 8.563
artist_hit_rate:playlist_subgenre[T.neo soul] -1.4755 3.629 -0.407 0.684 -8.589 5.638
artist_hit_rate:playlist_subgenre[T.new jack swing] 3.0457 11.189 0.272 0.785 -18.885 24.977
artist_hit_rate:playlist_subgenre[T.permanent wave] 5.6969 3.112 1.830 0.067 -0.404 11.797
artist_hit_rate:playlist_subgenre[T.pop edm] -1.7100 3.287 -0.520 0.603 -8.152 4.733
artist_hit_rate:playlist_subgenre[T.post-teen pop] 8.1730 3.062 2.669 0.008 2.171 14.175
artist_hit_rate:playlist_subgenre[T.progressive electro house] -0.3340 5.518 -0.061 0.952 -11.149 10.481
artist_hit_rate:playlist_subgenre[T.reggaeton] -0.9779 3.438 -0.284 0.776 -7.716 5.760
artist_hit_rate:playlist_subgenre[T.southern hip hop] -5.7172 3.613 -1.582 0.114 -12.799 1.365
artist_hit_rate:playlist_subgenre[T.trap] 1.2831 3.166 0.405 0.685 -4.923 7.490
artist_hit_rate:playlist_subgenre[T.tropical] 5.5766 3.654 1.526 0.127 -1.585 12.738
artist_hit_rate:playlist_subgenre[T.urban contemporary] 1.7476 3.036 0.576 0.565 -4.203 7.698
artist_n_tracks 4.8597 1.893 2.567 0.010 1.149 8.571
artist_n_tracks:playlist_subgenre[T.big room] 0.4271 2.592 0.165 0.869 -4.654 5.508
artist_n_tracks:playlist_subgenre[T.classic rock] -1.8724 2.599 -0.721 0.471 -6.966 3.221
artist_n_tracks:playlist_subgenre[T.dance pop] 0.8600 2.474 0.348 0.728 -3.989 5.709
artist_n_tracks:playlist_subgenre[T.electro house] -4.4776 2.380 -1.882 0.060 -9.142 0.186
artist_n_tracks:playlist_subgenre[T.electropop] -5.9169 2.491 -2.375 0.018 -10.799 -1.034
artist_n_tracks:playlist_subgenre[T.gangster rap] -5.0327 2.452 -2.053 0.040 -9.838 -0.227
artist_n_tracks:playlist_subgenre[T.hard rock] -4.1872 2.516 -1.664 0.096 -9.118 0.744
artist_n_tracks:playlist_subgenre[T.hip hop] -2.9106 2.680 -1.086 0.277 -8.163 2.342
artist_n_tracks:playlist_subgenre[T.hip pop] -0.1115 3.130 -0.036 0.972 -6.246 6.023
artist_n_tracks:playlist_subgenre[T.indie poptimism] -6.6103 2.511 -2.632 0.008 -11.533 -1.688
artist_n_tracks:playlist_subgenre[T.latin hip hop] -10.0671 2.553 -3.944 0.000 -15.070 -5.064
artist_n_tracks:playlist_subgenre[T.latin pop] -2.4894 2.660 -0.936 0.349 -7.703 2.724
artist_n_tracks:playlist_subgenre[T.neo soul] -4.1265 2.582 -1.598 0.110 -9.187 0.934
artist_n_tracks:playlist_subgenre[T.new jack swing] -3.4107 2.744 -1.243 0.214 -8.789 1.967
artist_n_tracks:playlist_subgenre[T.permanent wave] -3.9590 2.692 -1.471 0.141 -9.236 1.318
artist_n_tracks:playlist_subgenre[T.pop edm] -7.3842 2.644 -2.792 0.005 -12.567 -2.201
artist_n_tracks:playlist_subgenre[T.post-teen pop] -3.7995 2.577 -1.474 0.140 -8.851 1.252
artist_n_tracks:playlist_subgenre[T.progressive electro house] -7.6105 2.379 -3.199 0.001 -12.274 -2.947
artist_n_tracks:playlist_subgenre[T.reggaeton] -2.1574 2.908 -0.742 0.458 -7.857 3.542
artist_n_tracks:playlist_subgenre[T.southern hip hop] -2.6867 2.327 -1.155 0.248 -7.247 1.874
artist_n_tracks:playlist_subgenre[T.trap] -2.3264 2.762 -0.842 0.400 -7.741 3.088
artist_n_tracks:playlist_subgenre[T.tropical] -3.2632 2.812 -1.160 0.246 -8.776 2.249
artist_n_tracks:playlist_subgenre[T.urban contemporary] -2.2096 2.483 -0.890 0.374 -7.077 2.658
I(artist_avg_popularity ** 2) 5.5397 2.046 2.707 0.007 1.529 9.551
I(artist_avg_popularity ** 2):playlist_subgenre[T.big room] 6.3250 3.610 1.752 0.080 -0.751 13.401
I(artist_avg_popularity ** 2):playlist_subgenre[T.classic rock] 2.8588 2.717 1.052 0.293 -2.466 8.184
I(artist_avg_popularity ** 2):playlist_subgenre[T.dance pop] -0.5825 3.029 -0.192 0.847 -6.519 5.354
I(artist_avg_popularity ** 2):playlist_subgenre[T.electro house] 8.1731 2.989 2.734 0.006 2.314 14.032
I(artist_avg_popularity ** 2):playlist_subgenre[T.electropop] 6.2772 2.713 2.314 0.021 0.960 11.594
I(artist_avg_popularity ** 2):playlist_subgenre[T.gangster rap] 8.4024 2.780 3.022 0.003 2.953 13.852
I(artist_avg_popularity ** 2):playlist_subgenre[T.hard rock] 7.5232 2.725 2.761 0.006 2.182 12.865
I(artist_avg_popularity ** 2):playlist_subgenre[T.hip hop] -0.3300 4.110 -0.080 0.936 -8.386 7.726
I(artist_avg_popularity ** 2):playlist_subgenre[T.hip pop] 1.4659 2.892 0.507 0.612 -4.203 7.134
I(artist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism] 4.5982 2.485 1.851 0.064 -0.272 9.468
I(artist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop] 3.8441 2.710 1.419 0.156 -1.467 9.155
I(artist_avg_popularity ** 2):playlist_subgenre[T.latin pop] 3.3312 3.090 1.078 0.281 -2.725 9.387
I(artist_avg_popularity ** 2):playlist_subgenre[T.neo soul] 3.3444 2.630 1.272 0.204 -1.811 8.500
I(artist_avg_popularity ** 2):playlist_subgenre[T.new jack swing] 10.6749 3.986 2.678 0.007 2.862 18.487
I(artist_avg_popularity ** 2):playlist_subgenre[T.permanent wave] -1.2941 2.935 -0.441 0.659 -7.047 4.459
I(artist_avg_popularity ** 2):playlist_subgenre[T.pop edm] 4.1253 3.251 1.269 0.205 -2.247 10.498
I(artist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop] 0.2328 2.970 0.078 0.938 -5.589 6.055
I(artist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house] 8.1164 3.192 2.543 0.011 1.860 14.373
I(artist_avg_popularity ** 2):playlist_subgenre[T.reggaeton] 5.4154 6.809 0.795 0.426 -7.930 18.761
I(artist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop] 4.5167 2.623 1.722 0.085 -0.624 9.657
I(artist_avg_popularity ** 2):playlist_subgenre[T.trap] 0.4838 3.619 0.134 0.894 -6.610 7.578
I(artist_avg_popularity ** 2):playlist_subgenre[T.tropical] 5.0096 2.892 1.733 0.083 -0.658 10.677
I(artist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary] 3.8436 2.836 1.355 0.175 -1.715 9.403
I(playlist_avg_popularity ** 2) 5.2288 3.497 1.495 0.135 -1.626 12.084
I(playlist_avg_popularity ** 2):playlist_subgenre[T.big room] 3.7906 7.494 0.506 0.613 -10.898 18.479
I(playlist_avg_popularity ** 2):playlist_subgenre[T.classic rock] -4.8690 5.395 -0.902 0.367 -15.444 5.706
I(playlist_avg_popularity ** 2):playlist_subgenre[T.dance pop] 26.1758 37.709 0.694 0.488 -47.737 100.088
I(playlist_avg_popularity ** 2):playlist_subgenre[T.electro house] -3.9510 5.278 -0.749 0.454 -14.296 6.394
I(playlist_avg_popularity ** 2):playlist_subgenre[T.electropop] -1.9524 4.633 -0.421 0.673 -11.034 7.129
I(playlist_avg_popularity ** 2):playlist_subgenre[T.gangster rap] 10.9005 5.351 2.037 0.042 0.413 21.388
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hard rock] -1.0139 5.313 -0.191 0.849 -11.427 9.400
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip hop] 838.8790 430.775 1.947 0.052 -5.463 1683.221
I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip pop] 17.4270 11.418 1.526 0.127 -4.953 39.807
I(playlist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism] -8.6410 4.947 -1.747 0.081 -18.338 1.056
I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop] -0.2836 4.199 -0.068 0.946 -8.514 7.947
I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin pop] 7.8441 8.771 0.894 0.371 -9.348 25.037
I(playlist_avg_popularity ** 2):playlist_subgenre[T.neo soul] -8.4147 4.655 -1.808 0.071 -17.538 0.709
I(playlist_avg_popularity ** 2):playlist_subgenre[T.new jack swing] 1.0754 7.320 0.147 0.883 -13.271 15.422
I(playlist_avg_popularity ** 2):playlist_subgenre[T.permanent wave] -96.9527 20.161 -4.809 0.000 -136.470 -57.436
I(playlist_avg_popularity ** 2):playlist_subgenre[T.pop edm] 7.4560 5.027 1.483 0.138 -2.397 17.309
I(playlist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop] -85.2748 28.468 -2.995 0.003 -141.074 -29.476
I(playlist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house] 2.2438 7.292 0.308 0.758 -12.049 16.536
I(playlist_avg_popularity ** 2):playlist_subgenre[T.reggaeton] -0.0971 7.836 -0.012 0.990 -15.456 15.261
I(playlist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop] 8.9136 7.193 1.239 0.215 -5.185 23.013
I(playlist_avg_popularity ** 2):playlist_subgenre[T.trap] -18.8118 10.351 -1.817 0.069 -39.099 1.476
I(playlist_avg_popularity ** 2):playlist_subgenre[T.tropical] -26.6551 17.260 -1.544 0.123 -60.485 7.175
I(playlist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary] -0.7837 6.252 -0.125 0.900 -13.038 11.470
I(danceability ** 2) 0.4451 1.343 0.331 0.740 -2.187 3.077
I(danceability ** 2):playlist_subgenre[T.big room] 1.2908 2.113 0.611 0.541 -2.850 5.432
I(danceability ** 2):playlist_subgenre[T.classic rock] 2.7956 1.915 1.460 0.144 -0.957 6.548
I(danceability ** 2):playlist_subgenre[T.dance pop] -0.9468 1.955 -0.484 0.628 -4.779 2.885
I(danceability ** 2):playlist_subgenre[T.electro house] -0.1231 1.789 -0.069 0.945 -3.629 3.383
I(danceability ** 2):playlist_subgenre[T.electropop] 0.4802 1.769 0.271 0.786 -2.988 3.949
I(danceability ** 2):playlist_subgenre[T.gangster rap] -0.4261 1.847 -0.231 0.818 -4.047 3.195
I(danceability ** 2):playlist_subgenre[T.hard rock] 0.2264 2.010 0.113 0.910 -3.713 4.166
I(danceability ** 2):playlist_subgenre[T.hip hop] -0.7394 1.831 -0.404 0.686 -4.329 2.850
I(danceability ** 2):playlist_subgenre[T.hip pop] 1.4095 2.164 0.651 0.515 -2.832 5.651
I(danceability ** 2):playlist_subgenre[T.indie poptimism] -1.6100 1.726 -0.933 0.351 -4.992 1.772
I(danceability ** 2):playlist_subgenre[T.latin hip hop] -1.8534 1.965 -0.943 0.345 -5.704 1.997
I(danceability ** 2):playlist_subgenre[T.latin pop] 0.9238 2.040 0.453 0.651 -3.076 4.923
I(danceability ** 2):playlist_subgenre[T.neo soul] -0.7533 1.776 -0.424 0.671 -4.233 2.727
I(danceability ** 2):playlist_subgenre[T.new jack swing] -2.0662 2.169 -0.952 0.341 -6.318 2.186
I(danceability ** 2):playlist_subgenre[T.permanent wave] 0.7022 1.993 0.352 0.725 -3.204 4.608
I(danceability ** 2):playlist_subgenre[T.pop edm] -1.2356 2.153 -0.574 0.566 -5.457 2.985
I(danceability ** 2):playlist_subgenre[T.post-teen pop] -0.3384 2.027 -0.167 0.867 -4.311 3.634
I(danceability ** 2):playlist_subgenre[T.progressive electro house] -1.5256 1.860 -0.820 0.412 -5.172 2.120
I(danceability ** 2):playlist_subgenre[T.reggaeton] -4.7943 3.262 -1.470 0.142 -11.188 1.600
I(danceability ** 2):playlist_subgenre[T.southern hip hop] 0.3173 1.684 0.188 0.851 -2.984 3.619
I(danceability ** 2):playlist_subgenre[T.trap] 2.7282 1.855 1.470 0.141 -0.909 6.365
I(danceability ** 2):playlist_subgenre[T.tropical] -1.0741 1.874 -0.573 0.566 -4.747 2.599
I(danceability ** 2):playlist_subgenre[T.urban contemporary] -0.8839 1.771 -0.499 0.618 -4.355 2.587
I(energy ** 2) 0.9060 1.217 0.744 0.457 -1.480 3.292
I(energy ** 2):playlist_subgenre[T.big room] -1.5423 2.939 -0.525 0.600 -7.303 4.219
I(energy ** 2):playlist_subgenre[T.classic rock] 1.0782 2.089 0.516 0.606 -3.017 5.173
I(energy ** 2):playlist_subgenre[T.dance pop] -4.2859 2.045 -2.096 0.036 -8.294 -0.278
I(energy ** 2):playlist_subgenre[T.electro house] -1.0551 2.105 -0.501 0.616 -5.182 3.071
I(energy ** 2):playlist_subgenre[T.electropop] 1.8698 1.895 0.987 0.324 -1.845 5.584
I(energy ** 2):playlist_subgenre[T.gangster rap] -4.4047 2.216 -1.987 0.047 -8.749 -0.061
I(energy ** 2):playlist_subgenre[T.hard rock] -3.6187 2.395 -1.511 0.131 -8.313 1.076
I(energy ** 2):playlist_subgenre[T.hip hop] -0.9969 1.577 -0.632 0.527 -4.088 2.095
I(energy ** 2):playlist_subgenre[T.hip pop] 0.1497 2.009 0.075 0.941 -3.787 4.087
I(energy ** 2):playlist_subgenre[T.indie poptimism] -1.7426 1.560 -1.117 0.264 -4.799 1.314
I(energy ** 2):playlist_subgenre[T.latin hip hop] 0.5418 2.211 0.245 0.806 -3.792 4.876
I(energy ** 2):playlist_subgenre[T.latin pop] -3.3578 1.805 -1.861 0.063 -6.895 0.180
I(energy ** 2):playlist_subgenre[T.neo soul] -0.3453 1.596 -0.216 0.829 -3.473 2.782
I(energy ** 2):playlist_subgenre[T.new jack swing] -2.9113 2.006 -1.451 0.147 -6.844 1.021
I(energy ** 2):playlist_subgenre[T.permanent wave] -1.7455 1.732 -1.008 0.313 -5.139 1.648
I(energy ** 2):playlist_subgenre[T.pop edm] -1.2829 2.677 -0.479 0.632 -6.530 3.964
I(energy ** 2):playlist_subgenre[T.post-teen pop] -2.0306 1.862 -1.090 0.276 -5.681 1.619
I(energy ** 2):playlist_subgenre[T.progressive electro house] -2.6110 2.331 -1.120 0.263 -7.181 1.959
I(energy ** 2):playlist_subgenre[T.reggaeton] 4.0493 3.717 1.089 0.276 -3.236 11.335
I(energy ** 2):playlist_subgenre[T.southern hip hop] -4.3845 2.140 -2.049 0.041 -8.579 -0.190
I(energy ** 2):playlist_subgenre[T.trap] -1.6329 2.249 -0.726 0.468 -6.041 2.775
I(energy ** 2):playlist_subgenre[T.tropical] -1.2259 1.697 -0.723 0.470 -4.551 2.100
I(energy ** 2):playlist_subgenre[T.urban contemporary] 0.1291 1.572 0.082 0.935 -2.951 3.210
I(valence ** 2) -0.2305 1.599 -0.144 0.885 -3.364 2.903
I(valence ** 2):playlist_subgenre[T.big room] -1.5195 3.119 -0.487 0.626 -7.633 4.594
I(valence ** 2):playlist_subgenre[T.classic rock] 1.7124 2.191 0.781 0.435 -2.583 6.007
I(valence ** 2):playlist_subgenre[T.dance pop] -0.5040 2.180 -0.231 0.817 -4.778 3.770
I(valence ** 2):playlist_subgenre[T.electro house] -1.2812 2.238 -0.573 0.567 -5.667 3.105
I(valence ** 2):playlist_subgenre[T.electropop] 0.3732 2.156 0.173 0.863 -3.852 4.599
I(valence ** 2):playlist_subgenre[T.gangster rap] -3.1950 2.211 -1.445 0.148 -7.529 1.139
I(valence ** 2):playlist_subgenre[T.hard rock] 0.8121 2.339 0.347 0.728 -3.772 5.396
I(valence ** 2):playlist_subgenre[T.hip hop] 1.5009 2.180 0.688 0.491 -2.772 5.774
I(valence ** 2):playlist_subgenre[T.hip pop] -0.6172 2.456 -0.251 0.802 -5.430 4.196
I(valence ** 2):playlist_subgenre[T.indie poptimism] -0.7184 2.178 -0.330 0.742 -4.988 3.551
I(valence ** 2):playlist_subgenre[T.latin hip hop] 1.8771 2.164 0.867 0.386 -2.365 6.119
I(valence ** 2):playlist_subgenre[T.latin pop] 0.5438 2.179 0.250 0.803 -3.726 4.814
I(valence ** 2):playlist_subgenre[T.neo soul] 1.3429 2.099 0.640 0.522 -2.771 5.457
I(valence ** 2):playlist_subgenre[T.new jack swing] 1.0193 2.419 0.421 0.674 -3.723 5.761
I(valence ** 2):playlist_subgenre[T.permanent wave] 1.8104 2.270 0.798 0.425 -2.639 6.260
I(valence ** 2):playlist_subgenre[T.pop edm] 1.2543 2.403 0.522 0.602 -3.456 5.964
I(valence ** 2):playlist_subgenre[T.post-teen pop] 0.1665 2.259 0.074 0.941 -4.262 4.595
I(valence ** 2):playlist_subgenre[T.progressive electro house] -0.3411 2.245 -0.152 0.879 -4.741 4.059
I(valence ** 2):playlist_subgenre[T.reggaeton] 6.4864 3.379 1.919 0.055 -0.137 13.110
I(valence ** 2):playlist_subgenre[T.southern hip hop] 0.5741 2.069 0.278 0.781 -3.481 4.629
I(valence ** 2):playlist_subgenre[T.trap] -1.8127 2.340 -0.775 0.439 -6.399 2.774
I(valence ** 2):playlist_subgenre[T.tropical] -1.1656 2.188 -0.533 0.594 -5.454 3.123
I(valence ** 2):playlist_subgenre[T.urban contemporary] 1.7956 2.219 0.809 0.418 -2.554 6.145
I(tempo ** 2) -0.5728 0.885 -0.647 0.518 -2.307 1.162
I(tempo ** 2):playlist_subgenre[T.big room] 0.5618 2.329 0.241 0.809 -4.003 5.127
I(tempo ** 2):playlist_subgenre[T.classic rock] -0.3017 1.282 -0.235 0.814 -2.815 2.211
I(tempo ** 2):playlist_subgenre[T.dance pop] 1.3954 1.426 0.979 0.328 -1.400 4.190
I(tempo ** 2):playlist_subgenre[T.electro house] 1.2654 1.934 0.654 0.513 -2.526 5.056
I(tempo ** 2):playlist_subgenre[T.electropop] 1.4500 1.353 1.072 0.284 -1.201 4.101
I(tempo ** 2):playlist_subgenre[T.gangster rap] 0.5893 1.287 0.458 0.647 -1.933 3.111
I(tempo ** 2):playlist_subgenre[T.hard rock] 1.9941 1.347 1.480 0.139 -0.646 4.635
I(tempo ** 2):playlist_subgenre[T.hip hop] 0.3335 1.215 0.275 0.784 -2.048 2.715
I(tempo ** 2):playlist_subgenre[T.hip pop] 1.3406 1.402 0.956 0.339 -1.407 4.088
I(tempo ** 2):playlist_subgenre[T.indie poptimism] -1.6395 1.214 -1.350 0.177 -4.019 0.740
I(tempo ** 2):playlist_subgenre[T.latin hip hop] -0.5371 1.157 -0.464 0.642 -2.805 1.730
I(tempo ** 2):playlist_subgenre[T.latin pop] 1.8861 1.307 1.443 0.149 -0.675 4.447
I(tempo ** 2):playlist_subgenre[T.neo soul] 0.9525 1.193 0.798 0.425 -1.387 3.292
I(tempo ** 2):playlist_subgenre[T.new jack swing] 0.6557 1.389 0.472 0.637 -2.067 3.378
I(tempo ** 2):playlist_subgenre[T.permanent wave] 1.5071 1.308 1.152 0.249 -1.057 4.071
I(tempo ** 2):playlist_subgenre[T.pop edm] -0.7182 1.464 -0.491 0.624 -3.587 2.151
I(tempo ** 2):playlist_subgenre[T.post-teen pop] 3.4179 1.348 2.536 0.011 0.776 6.060
I(tempo ** 2):playlist_subgenre[T.progressive electro house] 2.4131 2.751 0.877 0.380 -2.979 7.805
I(tempo ** 2):playlist_subgenre[T.reggaeton] -1.3634 1.606 -0.849 0.396 -4.511 1.784
I(tempo ** 2):playlist_subgenre[T.southern hip hop] -1.4826 1.196 -1.239 0.215 -3.827 0.862
I(tempo ** 2):playlist_subgenre[T.trap] 1.6059 1.566 1.026 0.305 -1.463 4.675
I(tempo ** 2):playlist_subgenre[T.tropical] -0.5996 1.481 -0.405 0.686 -3.502 2.303
I(tempo ** 2):playlist_subgenre[T.urban contemporary] -0.3965 1.241 -0.320 0.749 -2.828 2.035
I(duration_ms ** 2) 0.2105 0.608 0.346 0.729 -0.981 1.402
I(duration_ms ** 2):playlist_subgenre[T.big room] -1.4170 1.470 -0.964 0.335 -4.298 1.464
I(duration_ms ** 2):playlist_subgenre[T.classic rock] 1.4702 1.133 1.298 0.194 -0.750 3.691
I(duration_ms ** 2):playlist_subgenre[T.dance pop] -0.2793 1.196 -0.234 0.815 -2.623 2.064
I(duration_ms ** 2):playlist_subgenre[T.electro house] -0.1904 0.786 -0.242 0.808 -1.730 1.349
I(duration_ms ** 2):playlist_subgenre[T.electropop] -0.9439 0.948 -0.996 0.319 -2.801 0.914
I(duration_ms ** 2):playlist_subgenre[T.gangster rap] -0.5102 1.025 -0.498 0.619 -2.518 1.498
I(duration_ms ** 2):playlist_subgenre[T.hard rock] -0.1488 0.950 -0.157 0.876 -2.012 1.714
I(duration_ms ** 2):playlist_subgenre[T.hip hop] 0.3458 0.959 0.361 0.718 -1.533 2.225
I(duration_ms ** 2):playlist_subgenre[T.hip pop] 0.6780 1.276 0.531 0.595 -1.822 3.178
I(duration_ms ** 2):playlist_subgenre[T.indie poptimism] -1.2139 1.170 -1.038 0.300 -3.507 1.079
I(duration_ms ** 2):playlist_subgenre[T.latin hip hop] 0.2607 0.896 0.291 0.771 -1.496 2.018
I(duration_ms ** 2):playlist_subgenre[T.latin pop] 0.0472 1.409 0.034 0.973 -2.715 2.810
I(duration_ms ** 2):playlist_subgenre[T.neo soul] 0.2432 0.845 0.288 0.773 -1.412 1.899
I(duration_ms ** 2):playlist_subgenre[T.new jack swing] -1.3907 1.303 -1.067 0.286 -3.945 1.163
I(duration_ms ** 2):playlist_subgenre[T.permanent wave] 0.6562 1.307 0.502 0.616 -1.906 3.219
I(duration_ms ** 2):playlist_subgenre[T.pop edm] -1.1728 1.350 -0.869 0.385 -3.818 1.473
I(duration_ms ** 2):playlist_subgenre[T.post-teen pop] 1.2663 1.273 0.995 0.320 -1.229 3.761
I(duration_ms ** 2):playlist_subgenre[T.progressive electro house] -0.0040 1.322 -0.003 0.998 -2.594 2.586
I(duration_ms ** 2):playlist_subgenre[T.reggaeton] 0.0045 1.448 0.003 0.998 -2.833 2.842
I(duration_ms ** 2):playlist_subgenre[T.southern hip hop] 0.6380 0.795 0.802 0.422 -0.920 2.196
I(duration_ms ** 2):playlist_subgenre[T.trap] 1.1207 1.164 0.963 0.336 -1.160 3.402
I(duration_ms ** 2):playlist_subgenre[T.tropical] 0.2269 1.049 0.216 0.829 -1.829 2.283
I(duration_ms ** 2):playlist_subgenre[T.urban contemporary] 0.1917 0.911 0.210 0.833 -1.594 1.978
I(artist_hit_rate ** 2) -4.5358 4.825 -0.940 0.347 -13.994 4.922
I(artist_hit_rate ** 2):playlist_subgenre[T.big room] 6.9241 8.504 0.814 0.416 -9.745 23.593
I(artist_hit_rate ** 2):playlist_subgenre[T.classic rock] 13.9855 6.622 2.112 0.035 1.006 26.965
I(artist_hit_rate ** 2):playlist_subgenre[T.dance pop] -7.2546 6.860 -1.058 0.290 -20.700 6.190
I(artist_hit_rate ** 2):playlist_subgenre[T.electro house] -15.2051 9.974 -1.524 0.127 -34.754 4.344
I(artist_hit_rate ** 2):playlist_subgenre[T.electropop] 2.3961 6.530 0.367 0.714 -10.403 15.196
I(artist_hit_rate ** 2):playlist_subgenre[T.gangster rap] 5.1983 6.337 0.820 0.412 -7.222 17.618
I(artist_hit_rate ** 2):playlist_subgenre[T.hard rock] -0.3423 6.756 -0.051 0.960 -13.585 12.900
I(artist_hit_rate ** 2):playlist_subgenre[T.hip hop] 7.8268 7.792 1.004 0.315 -7.447 23.100
I(artist_hit_rate ** 2):playlist_subgenre[T.hip pop] 9.7511 8.907 1.095 0.274 -7.708 27.210
I(artist_hit_rate ** 2):playlist_subgenre[T.indie poptimism] 17.9492 7.530 2.384 0.017 3.190 32.708
I(artist_hit_rate ** 2):playlist_subgenre[T.latin hip hop] 8.8263 7.373 1.197 0.231 -5.625 23.277
I(artist_hit_rate ** 2):playlist_subgenre[T.latin pop] 4.2054 7.200 0.584 0.559 -9.906 18.317
I(artist_hit_rate ** 2):playlist_subgenre[T.neo soul] 13.2709 7.534 1.762 0.078 -1.496 28.038
I(artist_hit_rate ** 2):playlist_subgenre[T.new jack swing] 13.8033 27.535 0.501 0.616 -40.167 67.773
I(artist_hit_rate ** 2):playlist_subgenre[T.permanent wave] -11.5700 7.456 -1.552 0.121 -26.184 3.044
I(artist_hit_rate ** 2):playlist_subgenre[T.pop edm] -1.3638 8.004 -0.170 0.865 -17.052 14.325
I(artist_hit_rate ** 2):playlist_subgenre[T.post-teen pop] -1.1403 6.883 -0.166 0.868 -14.631 12.350
I(artist_hit_rate ** 2):playlist_subgenre[T.progressive electro house] 11.5645 7.769 1.488 0.137 -3.664 26.793
I(artist_hit_rate ** 2):playlist_subgenre[T.reggaeton] 5.0538 6.827 0.740 0.459 -8.328 18.435
I(artist_hit_rate ** 2):playlist_subgenre[T.southern hip hop] -5.2627 6.439 -0.817 0.414 -17.884 7.358
I(artist_hit_rate ** 2):playlist_subgenre[T.trap] 6.4783 6.937 0.934 0.350 -7.119 20.075
I(artist_hit_rate ** 2):playlist_subgenre[T.tropical] 15.0845 8.334 1.810 0.070 -1.250 31.419
I(artist_hit_rate ** 2):playlist_subgenre[T.urban contemporary] -2.4634 7.432 -0.331 0.740 -17.030 12.103
I(artist_n_tracks ** 2) -5.8356 2.864 -2.038 0.042 -11.449 -0.223
I(artist_n_tracks ** 2):playlist_subgenre[T.big room] 7.3515 4.331 1.697 0.090 -1.137 15.841
I(artist_n_tracks ** 2):playlist_subgenre[T.classic rock] 13.5498 3.997 3.390 0.001 5.715 21.385
I(artist_n_tracks ** 2):playlist_subgenre[T.dance pop] 5.7474 4.018 1.430 0.153 -2.128 13.622
I(artist_n_tracks ** 2):playlist_subgenre[T.electro house] 6.3692 4.004 1.591 0.112 -1.478 14.217
I(artist_n_tracks ** 2):playlist_subgenre[T.electropop] 4.9822 3.859 1.291 0.197 -2.581 12.545
I(artist_n_tracks ** 2):playlist_subgenre[T.gangster rap] 7.4508 4.242 1.757 0.079 -0.863 15.765
I(artist_n_tracks ** 2):playlist_subgenre[T.hard rock] 3.9961 3.966 1.008 0.314 -3.777 11.769
I(artist_n_tracks ** 2):playlist_subgenre[T.hip hop] 3.3369 4.370 0.764 0.445 -5.229 11.903
I(artist_n_tracks ** 2):playlist_subgenre[T.hip pop] 11.1703 4.972 2.247 0.025 1.425 20.916
I(artist_n_tracks ** 2):playlist_subgenre[T.indie poptimism] 4.9672 4.019 1.236 0.216 -2.910 12.844
I(artist_n_tracks ** 2):playlist_subgenre[T.latin hip hop] 5.4074 4.146 1.304 0.192 -2.719 13.534
I(artist_n_tracks ** 2):playlist_subgenre[T.latin pop] 9.1134 4.388 2.077 0.038 0.513 17.714
I(artist_n_tracks ** 2):playlist_subgenre[T.neo soul] 4.6623 4.240 1.100 0.272 -3.648 12.973
I(artist_n_tracks ** 2):playlist_subgenre[T.new jack swing] 8.0327 5.042 1.593 0.111 -1.851 17.916
I(artist_n_tracks ** 2):playlist_subgenre[T.permanent wave] 4.5126 4.349 1.038 0.299 -4.011 13.036
I(artist_n_tracks ** 2):playlist_subgenre[T.pop edm] 10.8310 4.317 2.509 0.012 2.370 19.292
I(artist_n_tracks ** 2):playlist_subgenre[T.post-teen pop] 5.4403 3.984 1.365 0.172 -2.369 13.250
I(artist_n_tracks ** 2):playlist_subgenre[T.progressive electro house] 3.8962 3.935 0.990 0.322 -3.817 11.609
I(artist_n_tracks ** 2):playlist_subgenre[T.reggaeton] 6.6271 5.007 1.324 0.186 -3.186 16.440
I(artist_n_tracks ** 2):playlist_subgenre[T.southern hip hop] 2.3579 3.829 0.616 0.538 -5.148 9.863
I(artist_n_tracks ** 2):playlist_subgenre[T.trap] 8.4679 4.340 1.951 0.051 -0.038 16.974
I(artist_n_tracks ** 2):playlist_subgenre[T.tropical] 6.0892 4.703 1.295 0.195 -3.129 15.307
I(artist_n_tracks ** 2):playlist_subgenre[T.urban contemporary] 5.9166 4.225 1.400 0.161 -2.364 14.197
I(artist_avg_popularity ** 3) 3.9201 1.511 2.594 0.010 0.958 6.883
I(artist_avg_popularity ** 3):playlist_subgenre[T.big room] -1.9467 2.473 -0.787 0.431 -6.795 2.901
I(artist_avg_popularity ** 3):playlist_subgenre[T.classic rock] 0.4206 2.127 0.198 0.843 -3.749 4.590
I(artist_avg_popularity ** 3):playlist_subgenre[T.dance pop] -1.9528 1.934 -1.010 0.313 -5.743 1.837
I(artist_avg_popularity ** 3):playlist_subgenre[T.electro house] -2.5991 2.200 -1.182 0.237 -6.911 1.713
I(artist_avg_popularity ** 3):playlist_subgenre[T.electropop] -0.1635 1.932 -0.085 0.933 -3.951 3.623
I(artist_avg_popularity ** 3):playlist_subgenre[T.gangster rap] -0.9812 2.070 -0.474 0.635 -5.038 3.075
I(artist_avg_popularity ** 3):playlist_subgenre[T.hard rock] -0.2852 2.035 -0.140 0.889 -4.273 3.703
I(artist_avg_popularity ** 3):playlist_subgenre[T.hip hop] -0.2657 2.000 -0.133 0.894 -4.186 3.655
I(artist_avg_popularity ** 3):playlist_subgenre[T.hip pop] -3.0710 2.021 -1.520 0.129 -7.032 0.890
I(artist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism] -2.3894 1.828 -1.307 0.191 -5.972 1.193
I(artist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop] -3.0958 1.938 -1.598 0.110 -6.894 0.702
I(artist_avg_popularity ** 3):playlist_subgenre[T.latin pop] -4.6036 1.999 -2.303 0.021 -8.522 -0.685
I(artist_avg_popularity ** 3):playlist_subgenre[T.neo soul] -1.9739 1.860 -1.061 0.289 -5.619 1.671
I(artist_avg_popularity ** 3):playlist_subgenre[T.new jack swing] -0.8604 2.728 -0.315 0.752 -6.207 4.486
I(artist_avg_popularity ** 3):playlist_subgenre[T.permanent wave] -6.5769 2.000 -3.289 0.001 -10.497 -2.657
I(artist_avg_popularity ** 3):playlist_subgenre[T.pop edm] -0.1156 2.228 -0.052 0.959 -4.483 4.251
I(artist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop] -5.0715 1.899 -2.671 0.008 -8.793 -1.350
I(artist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house] -0.2674 2.127 -0.126 0.900 -4.436 3.901
I(artist_avg_popularity ** 3):playlist_subgenre[T.reggaeton] -1.2440 3.146 -0.395 0.693 -7.411 4.923
I(artist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop] -2.1137 1.927 -1.097 0.273 -5.890 1.662
I(artist_avg_popularity ** 3):playlist_subgenre[T.trap] -0.6778 2.138 -0.317 0.751 -4.869 3.513
I(artist_avg_popularity ** 3):playlist_subgenre[T.tropical] -2.3042 2.067 -1.115 0.265 -6.356 1.747
I(artist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary] -0.4825 1.944 -0.248 0.804 -4.294 3.328
I(playlist_avg_popularity ** 3) 0.8439 0.646 1.307 0.191 -0.422 2.110
I(playlist_avg_popularity ** 3):playlist_subgenre[T.big room] 20.3354 9.298 2.187 0.029 2.112 38.559
I(playlist_avg_popularity ** 3):playlist_subgenre[T.classic rock] -8.1745 3.566 -2.293 0.022 -15.164 -1.185
I(playlist_avg_popularity ** 3):playlist_subgenre[T.dance pop] -46.1502 42.763 -1.079 0.280 -129.967 37.667
I(playlist_avg_popularity ** 3):playlist_subgenre[T.electro house] 1.5047 1.702 0.884 0.377 -1.832 4.841
I(playlist_avg_popularity ** 3):playlist_subgenre[T.electropop] 0.1956 0.800 0.245 0.807 -1.372 1.763
I(playlist_avg_popularity ** 3):playlist_subgenre[T.gangster rap] 5.0763 2.035 2.494 0.013 1.087 9.066
I(playlist_avg_popularity ** 3):playlist_subgenre[T.hard rock] -1.0363 1.983 -0.522 0.601 -4.924 2.851
I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip hop] -523.2436 260.620 -2.008 0.045 -1034.072 -12.416
I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip pop] -8.3433 7.455 -1.119 0.263 -22.956 6.269
I(playlist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism] -0.1076 4.171 -0.026 0.979 -8.282 8.067
I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop] -0.3871 0.869 -0.446 0.656 -2.090 1.315
I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin pop] 1.1257 2.185 0.515 0.606 -3.156 5.408
I(playlist_avg_popularity ** 3):playlist_subgenre[T.neo soul] 0.1801 1.359 0.132 0.895 -2.484 2.844
I(playlist_avg_popularity ** 3):playlist_subgenre[T.new jack swing] 3.2099 8.194 0.392 0.695 -12.851 19.271
I(playlist_avg_popularity ** 3):playlist_subgenre[T.permanent wave] 139.1233 40.043 3.474 0.001 60.637 217.610
I(playlist_avg_popularity ** 3):playlist_subgenre[T.pop edm] 7.2999 3.629 2.012 0.044 0.187 14.413
I(playlist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop] 5.9622 2.823 2.112 0.035 0.429 11.495
I(playlist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house] -0.6997 4.494 -0.156 0.876 -9.509 8.109
I(playlist_avg_popularity ** 3):playlist_subgenre[T.reggaeton] -3.7654 3.942 -0.955 0.339 -11.492 3.961
I(playlist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop] 0.0337 2.293 0.015 0.988 -4.461 4.528
I(playlist_avg_popularity ** 3):playlist_subgenre[T.trap] 12.9336 16.376 0.790 0.430 -19.164 45.032
I(playlist_avg_popularity ** 3):playlist_subgenre[T.tropical] 43.5202 21.246 2.048 0.041 1.878 85.163
I(playlist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary] 5.9065 3.974 1.486 0.137 -1.883 13.696
I(danceability ** 3) 0.1990 0.385 0.517 0.605 -0.556 0.954
I(danceability ** 3):playlist_subgenre[T.big room] -0.2372 0.518 -0.458 0.647 -1.253 0.778
I(danceability ** 3):playlist_subgenre[T.classic rock] -0.0624 0.506 -0.123 0.902 -1.054 0.929
I(danceability ** 3):playlist_subgenre[T.dance pop] -0.2145 0.524 -0.409 0.682 -1.241 0.812
I(danceability ** 3):playlist_subgenre[T.electro house] -0.2529 0.653 -0.387 0.698 -1.532 1.026
I(danceability ** 3):playlist_subgenre[T.electropop] -0.5509 0.451 -1.222 0.222 -1.434 0.332
I(danceability ** 3):playlist_subgenre[T.gangster rap] 0.5042 0.652 0.773 0.439 -0.774 1.783
I(danceability ** 3):playlist_subgenre[T.hard rock] -0.4396 0.684 -0.643 0.520 -1.780 0.901
I(danceability ** 3):playlist_subgenre[T.hip hop] -0.6871 0.554 -1.239 0.215 -1.774 0.399
I(danceability ** 3):playlist_subgenre[T.hip pop] 0.1799 0.590 0.305 0.760 -0.976 1.336
I(danceability ** 3):playlist_subgenre[T.indie poptimism] 0.1569 0.445 0.353 0.724 -0.715 1.029
I(danceability ** 3):playlist_subgenre[T.latin hip hop] -1.1399 0.808 -1.412 0.158 -2.723 0.443
I(danceability ** 3):playlist_subgenre[T.latin pop] -0.1019 0.544 -0.187 0.851 -1.169 0.965
I(danceability ** 3):playlist_subgenre[T.neo soul] -0.1957 0.455 -0.430 0.667 -1.087 0.696
I(danceability ** 3):playlist_subgenre[T.new jack swing] 0.6583 0.976 0.674 0.500 -1.255 2.571
I(danceability ** 3):playlist_subgenre[T.permanent wave] 0.3969 0.539 0.736 0.462 -0.660 1.454
I(danceability ** 3):playlist_subgenre[T.pop edm] 0.0712 0.541 0.132 0.895 -0.990 1.132
I(danceability ** 3):playlist_subgenre[T.post-teen pop] -0.7596 0.504 -1.507 0.132 -1.748 0.229
I(danceability ** 3):playlist_subgenre[T.progressive electro house] -0.6631 0.573 -1.158 0.247 -1.786 0.459
I(danceability ** 3):playlist_subgenre[T.reggaeton] 3.2803 1.583 2.072 0.038 0.177 6.383
I(danceability ** 3):playlist_subgenre[T.southern hip hop] 0.1054 0.438 0.240 0.810 -0.754 0.965
I(danceability ** 3):playlist_subgenre[T.trap] 0.5929 0.574 1.032 0.302 -0.533 1.719
I(danceability ** 3):playlist_subgenre[T.tropical] -0.2886 0.490 -0.589 0.556 -1.249 0.672
I(danceability ** 3):playlist_subgenre[T.urban contemporary] -0.3655 0.440 -0.831 0.406 -1.228 0.497
I(energy ** 3) 0.3228 0.372 0.868 0.385 -0.406 1.052
I(energy ** 3):playlist_subgenre[T.big room] 0.5245 1.675 0.313 0.754 -2.759 3.808
I(energy ** 3):playlist_subgenre[T.classic rock] 0.2548 0.521 0.489 0.625 -0.766 1.276
I(energy ** 3):playlist_subgenre[T.dance pop] -0.5987 0.520 -1.151 0.250 -1.618 0.420
I(energy ** 3):playlist_subgenre[T.electro house] -0.4249 0.514 -0.827 0.408 -1.432 0.582
I(energy ** 3):playlist_subgenre[T.electropop] -0.9024 0.508 -1.776 0.076 -1.898 0.094
I(energy ** 3):playlist_subgenre[T.gangster rap] -0.3602 0.599 -0.602 0.547 -1.533 0.813
I(energy ** 3):playlist_subgenre[T.hard rock] -0.6087 0.559 -1.090 0.276 -1.704 0.486
I(energy ** 3):playlist_subgenre[T.hip hop] 0.1016 0.644 0.158 0.875 -1.161 1.364
I(energy ** 3):playlist_subgenre[T.hip pop] -0.4562 0.800 -0.570 0.569 -2.025 1.113
I(energy ** 3):playlist_subgenre[T.indie poptimism] 0.5312 0.571 0.930 0.353 -0.589 1.651
I(energy ** 3):playlist_subgenre[T.latin hip hop] -0.9984 0.569 -1.754 0.079 -2.114 0.117
I(energy ** 3):playlist_subgenre[T.latin pop] 0.2383 0.567 0.420 0.674 -0.873 1.349
I(energy ** 3):playlist_subgenre[T.neo soul] 0.3952 0.610 0.647 0.517 -0.801 1.592
I(energy ** 3):playlist_subgenre[T.new jack swing] -1.0457 0.562 -1.861 0.063 -2.147 0.055
I(energy ** 3):playlist_subgenre[T.permanent wave] -0.1735 0.530 -0.328 0.743 -1.211 0.864
I(energy ** 3):playlist_subgenre[T.pop edm] -0.5803 0.732 -0.793 0.428 -2.014 0.854
I(energy ** 3):playlist_subgenre[T.post-teen pop] -0.2599 0.551 -0.472 0.637 -1.340 0.820
I(energy ** 3):playlist_subgenre[T.progressive electro house] -1.6073 1.202 -1.337 0.181 -3.963 0.749
I(energy ** 3):playlist_subgenre[T.reggaeton] 4.4321 2.358 1.879 0.060 -0.190 9.055
I(energy ** 3):playlist_subgenre[T.southern hip hop] -0.3764 0.576 -0.654 0.513 -1.505 0.752
I(energy ** 3):playlist_subgenre[T.trap] -0.8413 0.573 -1.467 0.142 -1.965 0.283
I(energy ** 3):playlist_subgenre[T.tropical] -0.2376 0.589 -0.404 0.687 -1.391 0.916
I(energy ** 3):playlist_subgenre[T.urban contemporary] 0.0259 0.653 0.040 0.968 -1.255 1.306
I(valence ** 3) -0.4365 0.780 -0.559 0.576 -1.966 1.093
I(valence ** 3):playlist_subgenre[T.big room] 1.2427 1.083 1.148 0.251 -0.880 3.365
I(valence ** 3):playlist_subgenre[T.classic rock] -0.4502 1.209 -0.373 0.709 -2.819 1.919
I(valence ** 3):playlist_subgenre[T.dance pop] -0.7714 1.083 -0.712 0.476 -2.894 1.351
I(valence ** 3):playlist_subgenre[T.electro house] -0.0741 0.980 -0.076 0.940 -1.995 1.847
I(valence ** 3):playlist_subgenre[T.electropop] 0.0723 1.051 0.069 0.945 -1.988 2.133
I(valence ** 3):playlist_subgenre[T.gangster rap] 0.0234 1.023 0.023 0.982 -1.982 2.029
I(valence ** 3):playlist_subgenre[T.hard rock] 0.9972 1.129 0.883 0.377 -1.216 3.211
I(valence ** 3):playlist_subgenre[T.hip hop] 1.8362 1.050 1.748 0.080 -0.222 3.895
I(valence ** 3):playlist_subgenre[T.hip pop] 1.1960 1.204 0.994 0.320 -1.163 3.555
I(valence ** 3):playlist_subgenre[T.indie poptimism] 0.3733 0.998 0.374 0.708 -1.583 2.329
I(valence ** 3):playlist_subgenre[T.latin hip hop] 1.4700 1.186 1.239 0.215 -0.855 3.795
I(valence ** 3):playlist_subgenre[T.latin pop] 0.6063 1.207 0.502 0.615 -1.760 2.973
I(valence ** 3):playlist_subgenre[T.neo soul] -0.0436 1.056 -0.041 0.967 -2.114 2.026
I(valence ** 3):playlist_subgenre[T.new jack swing] 1.6914 1.399 1.209 0.227 -1.051 4.434
I(valence ** 3):playlist_subgenre[T.permanent wave] 1.0159 1.156 0.879 0.380 -1.250 3.282
I(valence ** 3):playlist_subgenre[T.pop edm] 0.9962 1.113 0.895 0.371 -1.186 3.178
I(valence ** 3):playlist_subgenre[T.post-teen pop] 0.0588 1.221 0.048 0.962 -2.335 2.452
I(valence ** 3):playlist_subgenre[T.progressive electro house] 0.2106 0.963 0.219 0.827 -1.677 2.099
I(valence ** 3):playlist_subgenre[T.reggaeton] -2.0878 1.896 -1.101 0.271 -5.804 1.629
I(valence ** 3):playlist_subgenre[T.southern hip hop] 0.7320 1.056 0.693 0.488 -1.338 2.802
I(valence ** 3):playlist_subgenre[T.trap] 0.8263 1.045 0.791 0.429 -1.222 2.875
I(valence ** 3):playlist_subgenre[T.tropical] -1.2864 1.049 -1.226 0.220 -3.343 0.771
I(valence ** 3):playlist_subgenre[T.urban contemporary] 1.3076 1.044 1.253 0.210 -0.738 3.353
I(tempo ** 3) 0.0515 0.125 0.411 0.681 -0.194 0.297
I(tempo ** 3):playlist_subgenre[T.big room] -0.3281 1.241 -0.264 0.792 -2.761 2.105
I(tempo ** 3):playlist_subgenre[T.classic rock] -0.3419 0.315 -1.087 0.277 -0.959 0.275
I(tempo ** 3):playlist_subgenre[T.dance pop] -0.0782 0.358 -0.219 0.827 -0.779 0.623
I(tempo ** 3):playlist_subgenre[T.electro house] -0.0251 0.783 -0.032 0.974 -1.561 1.510
I(tempo ** 3):playlist_subgenre[T.electropop] -0.3229 0.478 -0.675 0.500 -1.260 0.614
I(tempo ** 3):playlist_subgenre[T.gangster rap] -0.2686 0.314 -0.855 0.393 -0.884 0.347
I(tempo ** 3):playlist_subgenre[T.hard rock] -0.4763 0.490 -0.973 0.331 -1.436 0.483
I(tempo ** 3):playlist_subgenre[T.hip hop] -0.0762 0.196 -0.388 0.698 -0.461 0.309
I(tempo ** 3):playlist_subgenre[T.hip pop] 0.3039 0.333 0.913 0.361 -0.348 0.956
I(tempo ** 3):playlist_subgenre[T.indie poptimism] -0.5295 0.365 -1.450 0.147 -1.245 0.186
I(tempo ** 3):playlist_subgenre[T.latin hip hop] 0.1006 0.322 0.313 0.754 -0.530 0.731
I(tempo ** 3):playlist_subgenre[T.latin pop] -0.2120 0.442 -0.479 0.632 -1.079 0.655
I(tempo ** 3):playlist_subgenre[T.neo soul] -0.0467 0.224 -0.209 0.835 -0.485 0.392
I(tempo ** 3):playlist_subgenre[T.new jack swing] 0.1271 0.518 0.245 0.806 -0.889 1.143
I(tempo ** 3):playlist_subgenre[T.permanent wave] -0.1062 0.278 -0.382 0.702 -0.650 0.438
I(tempo ** 3):playlist_subgenre[T.pop edm] -0.0419 0.530 -0.079 0.937 -1.081 0.997
I(tempo ** 3):playlist_subgenre[T.post-teen pop] 0.0994 0.460 0.216 0.829 -0.802 1.001
I(tempo ** 3):playlist_subgenre[T.progressive electro house] 0.0730 1.332 0.055 0.956 -2.539 2.684
I(tempo ** 3):playlist_subgenre[T.reggaeton] -0.7172 0.649 -1.106 0.269 -1.989 0.554
I(tempo ** 3):playlist_subgenre[T.southern hip hop] -0.1978 0.282 -0.702 0.483 -0.751 0.355
I(tempo ** 3):playlist_subgenre[T.trap] 0.7734 0.654 1.183 0.237 -0.508 2.055
I(tempo ** 3):playlist_subgenre[T.tropical] -0.7687 0.528 -1.455 0.146 -1.804 0.267
I(tempo ** 3):playlist_subgenre[T.urban contemporary] 0.1227 0.358 0.343 0.732 -0.580 0.825
I(duration_ms ** 3) 0.1896 0.105 1.811 0.070 -0.016 0.395
I(duration_ms ** 3):playlist_subgenre[T.big room] -0.1102 0.711 -0.155 0.877 -1.503 1.283
I(duration_ms ** 3):playlist_subgenre[T.classic rock] -0.4854 0.322 -1.509 0.131 -1.116 0.145
I(duration_ms ** 3):playlist_subgenre[T.dance pop] -0.1882 0.504 -0.373 0.709 -1.177 0.801
I(duration_ms ** 3):playlist_subgenre[T.electro house] -0.1405 0.120 -1.168 0.243 -0.376 0.095
I(duration_ms ** 3):playlist_subgenre[T.electropop] 0.3583 0.292 1.226 0.220 -0.215 0.931
I(duration_ms ** 3):playlist_subgenre[T.gangster rap] -0.3174 0.213 -1.490 0.136 -0.735 0.100
I(duration_ms ** 3):playlist_subgenre[T.hard rock] -0.1468 0.309 -0.475 0.635 -0.753 0.459
I(duration_ms ** 3):playlist_subgenre[T.hip hop] -0.1190 0.174 -0.685 0.493 -0.460 0.222
I(duration_ms ** 3):playlist_subgenre[T.hip pop] -0.2361 0.220 -1.073 0.283 -0.667 0.195
I(duration_ms ** 3):playlist_subgenre[T.indie poptimism] -0.3843 0.492 -0.781 0.435 -1.349 0.580
I(duration_ms ** 3):playlist_subgenre[T.latin hip hop] -0.2322 0.207 -1.123 0.262 -0.637 0.173
I(duration_ms ** 3):playlist_subgenre[T.latin pop] -0.2180 0.365 -0.597 0.550 -0.934 0.498
I(duration_ms ** 3):playlist_subgenre[T.neo soul] -0.4898 0.221 -2.213 0.027 -0.924 -0.056
I(duration_ms ** 3):playlist_subgenre[T.new jack swing] -0.4285 0.188 -2.278 0.023 -0.797 -0.060
I(duration_ms ** 3):playlist_subgenre[T.permanent wave] 0.2006 0.428 0.469 0.639 -0.638 1.039
I(duration_ms ** 3):playlist_subgenre[T.pop edm] -0.6275 0.561 -1.119 0.263 -1.727 0.472
I(duration_ms ** 3):playlist_subgenre[T.post-teen pop] -0.6304 0.268 -2.356 0.018 -1.155 -0.106
I(duration_ms ** 3):playlist_subgenre[T.progressive electro house] 0.0054 0.283 0.019 0.985 -0.549 0.560
I(duration_ms ** 3):playlist_subgenre[T.reggaeton] 0.3751 0.583 0.643 0.520 -0.767 1.518
I(duration_ms ** 3):playlist_subgenre[T.southern hip hop] -0.2811 0.122 -2.295 0.022 -0.521 -0.041
I(duration_ms ** 3):playlist_subgenre[T.trap] 0.1298 0.412 0.315 0.753 -0.678 0.937
I(duration_ms ** 3):playlist_subgenre[T.tropical] -0.2456 0.188 -1.308 0.191 -0.614 0.123
I(duration_ms ** 3):playlist_subgenre[T.urban contemporary] -0.5350 0.218 -2.459 0.014 -0.961 -0.109
I(artist_hit_rate ** 3) 3.2005 2.885 1.109 0.267 -2.454 8.855
I(artist_hit_rate ** 3):playlist_subgenre[T.big room] -4.7891 8.628 -0.555 0.579 -21.700 12.121
I(artist_hit_rate ** 3):playlist_subgenre[T.classic rock] -10.0471 4.020 -2.499 0.012 -17.927 -2.168
I(artist_hit_rate ** 3):playlist_subgenre[T.dance pop] 2.2625 3.708 0.610 0.542 -5.005 9.530
I(artist_hit_rate ** 3):playlist_subgenre[T.electro house] 14.4122 7.847 1.837 0.066 -0.969 29.793
I(artist_hit_rate ** 3):playlist_subgenre[T.electropop] -0.3761 3.598 -0.105 0.917 -7.429 6.677
I(artist_hit_rate ** 3):playlist_subgenre[T.gangster rap] -3.7236 3.678 -1.012 0.311 -10.933 3.486
I(artist_hit_rate ** 3):playlist_subgenre[T.hard rock] -0.7139 4.116 -0.173 0.862 -8.781 7.353
I(artist_hit_rate ** 3):playlist_subgenre[T.hip hop] -6.2794 3.910 -1.606 0.108 -13.943 1.384
I(artist_hit_rate ** 3):playlist_subgenre[T.hip pop] -5.1457 4.507 -1.142 0.254 -13.979 3.688
I(artist_hit_rate ** 3):playlist_subgenre[T.indie poptimism] -10.3522 4.116 -2.515 0.012 -18.419 -2.285
I(artist_hit_rate ** 3):playlist_subgenre[T.latin hip hop] -3.7359 4.000 -0.934 0.350 -11.577 4.105
I(artist_hit_rate ** 3):playlist_subgenre[T.latin pop] -2.9068 3.804 -0.764 0.445 -10.362 4.548
I(artist_hit_rate ** 3):playlist_subgenre[T.neo soul] -6.0084 4.542 -1.323 0.186 -14.912 2.895
I(artist_hit_rate ** 3):playlist_subgenre[T.new jack swing] -6.4789 17.730 -0.365 0.715 -41.230 28.272
I(artist_hit_rate ** 3):playlist_subgenre[T.permanent wave] 2.5716 3.938 0.653 0.514 -5.147 10.290
I(artist_hit_rate ** 3):playlist_subgenre[T.pop edm] -1.0555 4.403 -0.240 0.811 -9.686 7.575
I(artist_hit_rate ** 3):playlist_subgenre[T.post-teen pop] -2.4475 3.617 -0.677 0.499 -9.538 4.643
I(artist_hit_rate ** 3):playlist_subgenre[T.progressive electro house] -5.9912 7.550 -0.794 0.427 -20.789 8.806
I(artist_hit_rate ** 3):playlist_subgenre[T.reggaeton] -2.8819 3.729 -0.773 0.440 -10.191 4.428
I(artist_hit_rate ** 3):playlist_subgenre[T.southern hip hop] 7.5348 4.543 1.659 0.097 -1.369 16.439
I(artist_hit_rate ** 3):playlist_subgenre[T.trap] -5.0470 3.710 -1.360 0.174 -12.318 2.224
I(artist_hit_rate ** 3):playlist_subgenre[T.tropical] -11.3145 4.720 -2.397 0.017 -20.565 -2.064
I(artist_hit_rate ** 3):playlist_subgenre[T.urban contemporary] -1.2146 3.830 -0.317 0.751 -8.721 6.292
I(artist_n_tracks ** 3) -1.2427 0.584 -2.128 0.033 -2.387 -0.098
I(artist_n_tracks ** 3):playlist_subgenre[T.big room] -0.2866 0.918 -0.312 0.755 -2.085 1.512
I(artist_n_tracks ** 3):playlist_subgenre[T.classic rock] -0.7137 0.827 -0.863 0.388 -2.334 0.907
I(artist_n_tracks ** 3):playlist_subgenre[T.dance pop] 0.7758 0.817 0.950 0.342 -0.825 2.376
I(artist_n_tracks ** 3):playlist_subgenre[T.electro house] 1.0229 0.881 1.162 0.245 -0.703 2.749
I(artist_n_tracks ** 3):playlist_subgenre[T.electropop] 1.6680 0.802 2.079 0.038 0.096 3.240
I(artist_n_tracks ** 3):playlist_subgenre[T.gangster rap] 1.1926 1.049 1.137 0.256 -0.864 3.249
I(artist_n_tracks ** 3):playlist_subgenre[T.hard rock] 1.0827 0.825 1.313 0.189 -0.533 2.699
I(artist_n_tracks ** 3):playlist_subgenre[T.hip hop] 1.7451 1.230 1.419 0.156 -0.666 4.156
I(artist_n_tracks ** 3):playlist_subgenre[T.hip pop] -1.3331 1.555 -0.857 0.391 -4.380 1.714
I(artist_n_tracks ** 3):playlist_subgenre[T.indie poptimism] 3.7295 1.187 3.141 0.002 1.402 6.057
I(artist_n_tracks ** 3):playlist_subgenre[T.latin hip hop] 3.2381 0.897 3.610 0.000 1.480 4.996
I(artist_n_tracks ** 3):playlist_subgenre[T.latin pop] 0.5250 0.976 0.538 0.590 -1.387 2.437
I(artist_n_tracks ** 3):playlist_subgenre[T.neo soul] 1.7630 1.597 1.104 0.270 -1.367 4.893
I(artist_n_tracks ** 3):playlist_subgenre[T.new jack swing] 0.2024 1.433 0.141 0.888 -2.607 3.012
I(artist_n_tracks ** 3):playlist_subgenre[T.permanent wave] 1.3165 0.948 1.389 0.165 -0.541 3.174
I(artist_n_tracks ** 3):playlist_subgenre[T.pop edm] 1.0125 0.935 1.084 0.279 -0.819 2.844
I(artist_n_tracks ** 3):playlist_subgenre[T.post-teen pop] 1.2006 0.842 1.426 0.154 -0.450 2.851
I(artist_n_tracks ** 3):playlist_subgenre[T.progressive electro house] 1.8730 0.827 2.265 0.024 0.252 3.494
I(artist_n_tracks ** 3):playlist_subgenre[T.reggaeton] 1.3049 0.991 1.316 0.188 -0.638 3.248
I(artist_n_tracks ** 3):playlist_subgenre[T.southern hip hop] 1.4305 0.841 1.701 0.089 -0.217 3.078
I(artist_n_tracks ** 3):playlist_subgenre[T.trap] 0.6050 1.173 0.516 0.606 -1.694 2.904
I(artist_n_tracks ** 3):playlist_subgenre[T.tropical] 0.6685 1.385 0.483 0.629 -2.046 3.383
I(artist_n_tracks ** 3):playlist_subgenre[T.urban contemporary] 1.5519 1.042 1.489 0.136 -0.491 3.595
artist_avg_popularity:I(artist_avg_popularity ** 2) 3.9201 1.511 2.594 0.010 0.958 6.883
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.big room] -1.9467 2.473 -0.787 0.431 -6.795 2.901
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.classic rock] 0.4206 2.127 0.198 0.843 -3.749 4.590
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.dance pop] -1.9528 1.934 -1.010 0.313 -5.743 1.837
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.electro house] -2.5991 2.200 -1.182 0.237 -6.911 1.713
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.electropop] -0.1635 1.932 -0.085 0.933 -3.951 3.623
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.gangster rap] -0.9812 2.070 -0.474 0.635 -5.038 3.075
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.hard rock] -0.2852 2.035 -0.140 0.889 -4.273 3.703
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.hip hop] -0.2657 2.000 -0.133 0.894 -4.186 3.655
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.hip pop] -3.0710 2.021 -1.520 0.129 -7.032 0.890
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism] -2.3894 1.828 -1.307 0.191 -5.972 1.193
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop] -3.0958 1.938 -1.598 0.110 -6.894 0.702
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.latin pop] -4.6036 1.999 -2.303 0.021 -8.522 -0.685
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.neo soul] -1.9739 1.860 -1.061 0.289 -5.619 1.671
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.new jack swing] -0.8604 2.728 -0.315 0.752 -6.207 4.486
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.permanent wave] -6.5769 2.000 -3.289 0.001 -10.497 -2.657
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.pop edm] -0.1156 2.228 -0.052 0.959 -4.483 4.251
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop] -5.0715 1.899 -2.671 0.008 -8.793 -1.350
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house] -0.2674 2.127 -0.126 0.900 -4.436 3.901
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.reggaeton] -1.2440 3.146 -0.395 0.693 -7.411 4.923
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop] -2.1137 1.927 -1.097 0.273 -5.890 1.662
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.trap] -0.6778 2.138 -0.317 0.751 -4.869 3.513
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.tropical] -2.3042 2.067 -1.115 0.265 -6.356 1.747
artist_avg_popularity:I(artist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary] -0.4825 1.944 -0.248 0.804 -4.294 3.328
artist_avg_popularity:I(artist_avg_popularity ** 3) 3.8379 1.579 2.431 0.015 0.743 6.933
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.big room] -3.2219 2.326 -1.385 0.166 -7.780 1.336
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.classic rock] -0.3047 2.127 -0.143 0.886 -4.474 3.865
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.dance pop] -2.0866 2.192 -0.952 0.341 -6.383 2.210
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.electro house] -4.5854 2.205 -2.079 0.038 -8.908 -0.263
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.electropop] -1.5439 1.993 -0.775 0.439 -5.451 2.363
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.gangster rap] -2.4016 2.058 -1.167 0.243 -6.435 1.632
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.hard rock] -1.4115 2.130 -0.663 0.508 -5.587 2.764
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.hip hop] -0.8678 2.912 -0.298 0.766 -6.576 4.841
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.hip pop] -3.3700 2.167 -1.555 0.120 -7.618 0.878
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism] -3.2625 1.882 -1.734 0.083 -6.951 0.426
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop] -3.8021 1.999 -1.902 0.057 -7.720 0.116
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.latin pop] -4.9887 2.291 -2.178 0.029 -9.479 -0.499
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.neo soul] -2.6462 1.841 -1.437 0.151 -6.255 0.963
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.new jack swing] -2.7996 2.532 -1.106 0.269 -7.762 2.163
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.permanent wave] -6.5834 2.238 -2.941 0.003 -10.971 -2.196
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.pop edm] -0.7018 2.336 -0.300 0.764 -5.281 3.877
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop] -5.2663 2.121 -2.483 0.013 -9.424 -1.108
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house] -1.9180 1.995 -0.961 0.336 -5.828 1.992
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.reggaeton] -2.5725 4.172 -0.617 0.537 -10.749 5.604
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop] -2.9554 1.974 -1.497 0.134 -6.824 0.913
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.trap] -1.0255 2.561 -0.400 0.689 -6.046 3.995
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.tropical] -3.2578 2.234 -1.458 0.145 -7.637 1.121
artist_avg_popularity:I(artist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary] -1.5730 2.086 -0.754 0.451 -5.661 2.515
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3) 0.5164 0.222 2.330 0.020 0.082 0.951
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.big room] -0.4908 0.312 -1.575 0.115 -1.102 0.120
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.classic rock] -0.0847 0.290 -0.292 0.770 -0.653 0.484
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.dance pop] -0.2951 0.320 -0.922 0.356 -0.922 0.332
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.electro house] -0.7152 0.303 -2.362 0.018 -1.309 -0.122
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.electropop] -0.2825 0.278 -1.018 0.309 -0.827 0.262
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.gangster rap] -0.3767 0.284 -1.325 0.185 -0.934 0.181
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.hard rock] -0.2323 0.299 -0.777 0.437 -0.818 0.353
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.hip hop] -0.1965 0.551 -0.357 0.721 -1.276 0.883
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.hip pop] -0.4590 0.306 -1.502 0.133 -1.058 0.140
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism] -0.4689 0.262 -1.793 0.073 -0.981 0.044
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop] -0.5330 0.280 -1.901 0.057 -1.083 0.017
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.latin pop] -0.6591 0.341 -1.931 0.054 -1.328 0.010
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.neo soul] -0.3831 0.253 -1.516 0.130 -0.879 0.112
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.new jack swing] -0.4571 0.339 -1.347 0.178 -1.122 0.208
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.permanent wave] -0.8780 0.327 -2.684 0.007 -1.519 -0.237
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.pop edm] -0.1210 0.325 -0.372 0.710 -0.758 0.516
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop] -0.7083 0.309 -2.292 0.022 -1.314 -0.103
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house] -0.3369 0.269 -1.254 0.210 -0.864 0.190
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.reggaeton] -0.4128 0.603 -0.685 0.494 -1.595 0.769
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop] -0.4300 0.275 -1.563 0.118 -0.969 0.109
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.trap] -0.1769 0.382 -0.462 0.644 -0.927 0.573
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.tropical] -0.4792 0.321 -1.491 0.136 -1.109 0.151
I(artist_avg_popularity ** 2):I(artist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary] -0.2829 0.296 -0.954 0.340 -0.864 0.298
playlist_avg_popularity:I(playlist_avg_popularity ** 2) 0.8439 0.646 1.307 0.191 -0.422 2.110
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.big room] 20.3354 9.298 2.187 0.029 2.112 38.559
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.classic rock] -8.1745 3.566 -2.293 0.022 -15.164 -1.185
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.dance pop] -46.1502 42.763 -1.079 0.280 -129.967 37.667
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.electro house] 1.5047 1.702 0.884 0.377 -1.832 4.841
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.electropop] 0.1956 0.800 0.245 0.807 -1.372 1.763
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.gangster rap] 5.0763 2.035 2.494 0.013 1.087 9.066
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.hard rock] -1.0363 1.983 -0.522 0.601 -4.924 2.851
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip hop] -523.2436 260.620 -2.008 0.045 -1034.072 -12.416
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.hip pop] -8.3433 7.455 -1.119 0.263 -22.956 6.269
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.indie poptimism] -0.1076 4.171 -0.026 0.979 -8.282 8.067
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin hip hop] -0.3871 0.869 -0.446 0.656 -2.090 1.315
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.latin pop] 1.1257 2.185 0.515 0.606 -3.156 5.408
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.neo soul] 0.1801 1.359 0.132 0.895 -2.484 2.844
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.new jack swing] 3.2099 8.194 0.392 0.695 -12.851 19.271
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.permanent wave] 139.1233 40.043 3.474 0.001 60.637 217.610
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.pop edm] 7.2999 3.629 2.012 0.044 0.187 14.413
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.post-teen pop] 5.9622 2.823 2.112 0.035 0.429 11.495
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.progressive electro house] -0.6997 4.494 -0.156 0.876 -9.509 8.109
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.reggaeton] -3.7654 3.942 -0.955 0.339 -11.492 3.961
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.southern hip hop] 0.0337 2.293 0.015 0.988 -4.461 4.528
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.trap] 12.9336 16.376 0.790 0.430 -19.164 45.032
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.tropical] 43.5202 21.246 2.048 0.041 1.878 85.163
playlist_avg_popularity:I(playlist_avg_popularity ** 2):playlist_subgenre[T.urban contemporary] 5.9065 3.974 1.486 0.137 -1.883 13.696
playlist_avg_popularity:I(playlist_avg_popularity ** 3) 0.9685 1.925 0.503 0.615 -2.805 4.742
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.big room] 28.9964 12.559 2.309 0.021 4.380 53.613
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.classic rock] 5.3943 3.703 1.457 0.145 -1.864 12.652
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.dance pop] 82.5944 69.888 1.182 0.237 -54.389 219.578
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.electro house] 3.6027 4.164 0.865 0.387 -4.559 11.765
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.electropop] 0.3086 2.397 0.129 0.898 -4.389 5.006
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.gangster rap] -10.8337 3.265 -3.318 0.001 -17.234 -4.433
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.hard rock] -3.5263 4.740 -0.744 0.457 -12.818 5.765
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip hop] 586.8161 289.253 2.029 0.042 19.865 1153.767
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip pop] -14.2595 7.257 -1.965 0.049 -28.484 -0.035
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism] 2.4707 2.838 0.871 0.384 -3.092 8.034
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop] -1.0344 2.327 -0.444 0.657 -5.596 3.527
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin pop] -11.6439 8.915 -1.306 0.192 -29.117 5.829
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.neo soul] 3.8562 3.356 1.149 0.251 -2.722 10.434
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.new jack swing] -5.2009 15.943 -0.326 0.744 -36.449 26.047
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.permanent wave] -247.8851 86.565 -2.864 0.004 -417.558 -78.212
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.pop edm] -8.1664 2.626 -3.110 0.002 -13.314 -3.019
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop] 46.9376 16.078 2.919 0.004 15.425 78.451
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house] -2.4659 4.604 -0.536 0.592 -11.490 6.559
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.reggaeton] -3.2323 4.867 -0.664 0.507 -12.771 6.306
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop] -14.8098 8.171 -1.812 0.070 -30.826 1.206
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.trap] -7.3908 51.361 -0.144 0.886 -108.061 93.280
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.tropical] 16.3813 19.498 0.840 0.401 -21.836 54.598
playlist_avg_popularity:I(playlist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary] -2.0841 2.863 -0.728 0.467 -7.695 3.527
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3) 0.1623 0.393 0.413 0.679 -0.608 0.932
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.big room] 5.7496 2.456 2.341 0.019 0.935 10.564
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.classic rock] 10.5957 4.156 2.550 0.011 2.450 18.741
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.dance pop] -23.6436 18.887 -1.252 0.211 -60.664 13.376
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.electro house] 1.0371 1.045 0.992 0.321 -1.012 3.086
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.electropop] 0.1411 0.551 0.256 0.798 -0.939 1.221
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.gangster rap] -7.2674 1.968 -3.693 0.000 -11.125 -3.410
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.hard rock] -0.8214 1.070 -0.767 0.443 -2.920 1.277
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip hop] -122.1359 59.733 -2.045 0.041 -239.216 -5.056
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.hip pop] 10.9449 7.831 1.398 0.162 -4.403 26.293
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.indie poptimism] -0.9648 4.461 -0.216 0.829 -9.708 7.779
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin hip hop] -0.1786 0.457 -0.391 0.696 -1.075 0.718
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.latin pop] 3.4410 4.140 0.831 0.406 -4.674 11.556
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.neo soul] 0.8469 0.663 1.276 0.202 -0.454 2.147
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.new jack swing] -4.0294 4.610 -0.874 0.382 -13.065 5.006
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.permanent wave] 71.4682 28.834 2.479 0.013 14.953 127.983
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.pop edm] -8.9968 2.968 -3.031 0.002 -14.814 -3.180
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.post-teen pop] -20.8071 6.830 -3.046 0.002 -34.195 -7.420
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.progressive electro house] -0.5112 0.742 -0.689 0.491 -1.966 0.943
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.reggaeton] 2.1228 3.706 0.573 0.567 -5.141 9.386
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.southern hip hop] -7.1547 4.207 -1.701 0.089 -15.400 1.091
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.trap] -4.3697 21.119 -0.207 0.836 -45.764 37.025
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.tropical] -94.2655 50.626 -1.862 0.063 -193.495 4.964
I(playlist_avg_popularity ** 2):I(playlist_avg_popularity ** 3):playlist_subgenre[T.urban contemporary] -4.9454 3.241 -1.526 0.127 -11.297 1.406
danceability:I(danceability ** 2) 0.1990 0.385 0.517 0.605 -0.556 0.954
danceability:I(danceability ** 2):playlist_subgenre[T.big room] -0.2372 0.518 -0.458 0.647 -1.253 0.778
danceability:I(danceability ** 2):playlist_subgenre[T.classic rock] -0.0624 0.506 -0.123 0.902 -1.054 0.929
danceability:I(danceability ** 2):playlist_subgenre[T.dance pop] -0.2145 0.524 -0.409 0.682 -1.241 0.812
danceability:I(danceability ** 2):playlist_subgenre[T.electro house] -0.2529 0.653 -0.387 0.698 -1.532 1.026
danceability:I(danceability ** 2):playlist_subgenre[T.electropop] -0.5509 0.451 -1.222 0.222 -1.434 0.332
danceability:I(danceability ** 2):playlist_subgenre[T.gangster rap] 0.5042 0.652 0.773 0.439 -0.774 1.783
danceability:I(danceability ** 2):playlist_subgenre[T.hard rock] -0.4396 0.684 -0.643 0.520 -1.780 0.901
danceability:I(danceability ** 2):playlist_subgenre[T.hip hop] -0.6871 0.554 -1.239 0.215 -1.774 0.399
danceability:I(danceability ** 2):playlist_subgenre[T.hip pop] 0.1799 0.590 0.305 0.760 -0.976 1.336
danceability:I(danceability ** 2):playlist_subgenre[T.indie poptimism] 0.1569 0.445 0.353 0.724 -0.715 1.029
danceability:I(danceability ** 2):playlist_subgenre[T.latin hip hop] -1.1399 0.808 -1.412 0.158 -2.723 0.443
danceability:I(danceability ** 2):playlist_subgenre[T.latin pop] -0.1019 0.544 -0.187 0.851 -1.169 0.965
danceability:I(danceability ** 2):playlist_subgenre[T.neo soul] -0.1957 0.455 -0.430 0.667 -1.087 0.696
danceability:I(danceability ** 2):playlist_subgenre[T.new jack swing] 0.6583 0.976 0.674 0.500 -1.255 2.571
danceability:I(danceability ** 2):playlist_subgenre[T.permanent wave] 0.3969 0.539 0.736 0.462 -0.660 1.454
danceability:I(danceability ** 2):playlist_subgenre[T.pop edm] 0.0712 0.541 0.132 0.895 -0.990 1.132
danceability:I(danceability ** 2):playlist_subgenre[T.post-teen pop] -0.7596 0.504 -1.507 0.132 -1.748 0.229
danceability:I(danceability ** 2):playlist_subgenre[T.progressive electro house] -0.6631 0.573 -1.158 0.247 -1.786 0.459
danceability:I(danceability ** 2):playlist_subgenre[T.reggaeton] 3.2803 1.583 2.072 0.038 0.177 6.383
danceability:I(danceability ** 2):playlist_subgenre[T.southern hip hop] 0.1054 0.438 0.240 0.810 -0.754 0.965
danceability:I(danceability ** 2):playlist_subgenre[T.trap] 0.5929 0.574 1.032 0.302 -0.533 1.719
danceability:I(danceability ** 2):playlist_subgenre[T.tropical] -0.2886 0.490 -0.589 0.556 -1.249 0.672
danceability:I(danceability ** 2):playlist_subgenre[T.urban contemporary] -0.3655 0.440 -0.831 0.406 -1.228 0.497
danceability:I(danceability ** 3) 0.2799 0.541 0.517 0.605 -0.781 1.341
danceability:I(danceability ** 3):playlist_subgenre[T.big room] -0.6923 0.818 -0.847 0.397 -2.295 0.910
danceability:I(danceability ** 3):playlist_subgenre[T.classic rock] -0.9564 0.737 -1.297 0.195 -2.402 0.489
danceability:I(danceability ** 3):playlist_subgenre[T.dance pop] 0.3606 0.752 0.479 0.632 -1.114 1.835
danceability:I(danceability ** 3):playlist_subgenre[T.electro house] -0.3183 0.647 -0.492 0.623 -1.586 0.949
danceability:I(danceability ** 3):playlist_subgenre[T.electropop] -0.6581 0.655 -1.004 0.315 -1.942 0.626
danceability:I(danceability ** 3):playlist_subgenre[T.gangster rap] -0.3219 0.678 -0.475 0.635 -1.650 1.006
danceability:I(danceability ** 3):playlist_subgenre[T.hard rock] -0.5167 0.814 -0.635 0.526 -2.112 1.079
danceability:I(danceability ** 3):playlist_subgenre[T.hip hop] -0.0091 0.658 -0.014 0.989 -1.299 1.281
danceability:I(danceability ** 3):playlist_subgenre[T.hip pop] -1.0148 0.785 -1.293 0.196 -2.553 0.523
danceability:I(danceability ** 3):playlist_subgenre[T.indie poptimism] 0.0284 0.651 0.044 0.965 -1.247 1.304
danceability:I(danceability ** 3):playlist_subgenre[T.latin hip hop] 0.1980 0.697 0.284 0.776 -1.169 1.565
danceability:I(danceability ** 3):playlist_subgenre[T.latin pop] -0.6707 0.747 -0.897 0.370 -2.136 0.794
danceability:I(danceability ** 3):playlist_subgenre[T.neo soul] -0.3944 0.670 -0.588 0.556 -1.709 0.920
danceability:I(danceability ** 3):playlist_subgenre[T.new jack swing] 0.0957 0.786 0.122 0.903 -1.445 1.636
danceability:I(danceability ** 3):playlist_subgenre[T.permanent wave] -0.1407 0.765 -0.184 0.854 -1.639 1.358
danceability:I(danceability ** 3):playlist_subgenre[T.pop edm] 0.3297 0.813 0.405 0.685 -1.265 1.924
danceability:I(danceability ** 3):playlist_subgenre[T.post-teen pop] -0.0227 0.748 -0.030 0.976 -1.490 1.444
danceability:I(danceability ** 3):playlist_subgenre[T.progressive electro house] 0.1922 0.685 0.281 0.779 -1.151 1.535
danceability:I(danceability ** 3):playlist_subgenre[T.reggaeton] 0.8490 1.064 0.798 0.425 -1.236 2.934
danceability:I(danceability ** 3):playlist_subgenre[T.southern hip hop] -0.4102 0.608 -0.675 0.500 -1.602 0.782
danceability:I(danceability ** 3):playlist_subgenre[T.trap] -1.1495 0.668 -1.722 0.085 -2.458 0.159
danceability:I(danceability ** 3):playlist_subgenre[T.tropical] -0.1323 0.695 -0.191 0.849 -1.494 1.229
danceability:I(danceability ** 3):playlist_subgenre[T.urban contemporary] 0.0021 0.649 0.003 0.997 -1.270 1.274
I(danceability ** 2):I(danceability ** 3) 0.0557 0.096 0.580 0.562 -0.133 0.244
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.big room] -0.1333 0.164 -0.815 0.415 -0.454 0.187
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.classic rock] -0.2112 0.136 -1.548 0.122 -0.479 0.056
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.dance pop] 0.1244 0.181 0.688 0.491 -0.230 0.479
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.electro house] -0.0387 0.217 -0.179 0.858 -0.464 0.386
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.electropop] -0.1027 0.117 -0.874 0.382 -0.333 0.128
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.gangster rap] -0.2272 0.218 -1.042 0.298 -0.655 0.200
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.hard rock] -0.0958 0.134 -0.716 0.474 -0.358 0.166
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.hip hop] 0.1198 0.171 0.698 0.485 -0.216 0.456
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.hip pop] -0.3297 0.212 -1.556 0.120 -0.745 0.086
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.indie poptimism] -0.0410 0.122 -0.337 0.736 -0.280 0.198
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.latin hip hop] 0.2462 0.292 0.843 0.399 -0.326 0.818
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.latin pop] -0.1553 0.189 -0.821 0.412 -0.526 0.216
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.neo soul] -0.0870 0.135 -0.645 0.519 -0.351 0.177
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.new jack swing] -0.3498 0.392 -0.893 0.372 -1.117 0.418
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.permanent wave] -0.0811 0.141 -0.575 0.565 -0.358 0.195
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.pop edm] 0.0702 0.198 0.355 0.722 -0.317 0.458
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.post-teen pop] 0.1227 0.175 0.701 0.483 -0.220 0.466
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.progressive electro house] 0.1717 0.197 0.870 0.384 -0.215 0.559
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.reggaeton] -1.8213 0.737 -2.471 0.013 -3.266 -0.376
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.southern hip hop] -0.1206 0.121 -1.000 0.317 -0.357 0.116
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.trap] -0.3846 0.184 -2.089 0.037 -0.745 -0.024
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.tropical] -0.0286 0.123 -0.234 0.815 -0.269 0.212
I(danceability ** 2):I(danceability ** 3):playlist_subgenre[T.urban contemporary] 0.0347 0.123 0.283 0.777 -0.206 0.275
energy:I(energy ** 2) 0.3228 0.372 0.868 0.385 -0.406 1.052
energy:I(energy ** 2):playlist_subgenre[T.big room] 0.5245 1.675 0.313 0.754 -2.759 3.808
energy:I(energy ** 2):playlist_subgenre[T.classic rock] 0.2548 0.521 0.489 0.625 -0.766 1.276
energy:I(energy ** 2):playlist_subgenre[T.dance pop] -0.5987 0.520 -1.151 0.250 -1.618 0.420
energy:I(energy ** 2):playlist_subgenre[T.electro house] -0.4249 0.514 -0.827 0.408 -1.432 0.582
energy:I(energy ** 2):playlist_subgenre[T.electropop] -0.9024 0.508 -1.776 0.076 -1.898 0.094
energy:I(energy ** 2):playlist_subgenre[T.gangster rap] -0.3602 0.599 -0.602 0.547 -1.533 0.813
energy:I(energy ** 2):playlist_subgenre[T.hard rock] -0.6087 0.559 -1.090 0.276 -1.704 0.486
energy:I(energy ** 2):playlist_subgenre[T.hip hop] 0.1016 0.644 0.158 0.875 -1.161 1.364
energy:I(energy ** 2):playlist_subgenre[T.hip pop] -0.4562 0.800 -0.570 0.569 -2.025 1.113
energy:I(energy ** 2):playlist_subgenre[T.indie poptimism] 0.5312 0.571 0.930 0.353 -0.589 1.651
energy:I(energy ** 2):playlist_subgenre[T.latin hip hop] -0.9984 0.569 -1.754 0.079 -2.114 0.117
energy:I(energy ** 2):playlist_subgenre[T.latin pop] 0.2383 0.567 0.420 0.674 -0.873 1.349
energy:I(energy ** 2):playlist_subgenre[T.neo soul] 0.3952 0.610 0.647 0.517 -0.801 1.592
energy:I(energy ** 2):playlist_subgenre[T.new jack swing] -1.0457 0.562 -1.861 0.063 -2.147 0.055
energy:I(energy ** 2):playlist_subgenre[T.permanent wave] -0.1735 0.530 -0.328 0.743 -1.211 0.864
energy:I(energy ** 2):playlist_subgenre[T.pop edm] -0.5803 0.732 -0.793 0.428 -2.014 0.854
energy:I(energy ** 2):playlist_subgenre[T.post-teen pop] -0.2599 0.551 -0.472 0.637 -1.340 0.820
energy:I(energy ** 2):playlist_subgenre[T.progressive electro house] -1.6073 1.202 -1.337 0.181 -3.963 0.749
energy:I(energy ** 2):playlist_subgenre[T.reggaeton] 4.4321 2.358 1.879 0.060 -0.190 9.055
energy:I(energy ** 2):playlist_subgenre[T.southern hip hop] -0.3764 0.576 -0.654 0.513 -1.505 0.752
energy:I(energy ** 2):playlist_subgenre[T.trap] -0.8413 0.573 -1.467 0.142 -1.965 0.283
energy:I(energy ** 2):playlist_subgenre[T.tropical] -0.2376 0.589 -0.404 0.687 -1.391 0.916
energy:I(energy ** 2):playlist_subgenre[T.urban contemporary] 0.0259 0.653 0.040 0.968 -1.255 1.306
energy:I(energy ** 3) 0.0166 0.538 0.031 0.975 -1.039 1.072
energy:I(energy ** 3):playlist_subgenre[T.big room] -0.6977 1.241 -0.562 0.574 -3.130 1.735
energy:I(energy ** 3):playlist_subgenre[T.classic rock] -1.1211 0.941 -1.192 0.233 -2.965 0.723
energy:I(energy ** 3):playlist_subgenre[T.dance pop] 0.9447 0.897 1.054 0.292 -0.813 2.702
energy:I(energy ** 3):playlist_subgenre[T.electro house] -0.1216 0.872 -0.139 0.889 -1.831 1.588
energy:I(energy ** 3):playlist_subgenre[T.electropop] -1.3110 0.830 -1.580 0.114 -2.937 0.315
energy:I(energy ** 3):playlist_subgenre[T.gangster rap] 1.6094 1.156 1.392 0.164 -0.657 3.876
energy:I(energy ** 3):playlist_subgenre[T.hard rock] 0.6962 0.929 0.750 0.453 -1.124 2.516
energy:I(energy ** 3):playlist_subgenre[T.hip hop] 0.5663 0.758 0.747 0.455 -0.920 2.052
energy:I(energy ** 3):playlist_subgenre[T.hip pop] -0.2687 1.105 -0.243 0.808 -2.435 1.897
energy:I(energy ** 3):playlist_subgenre[T.indie poptimism] 0.8189 0.765 1.070 0.285 -0.681 2.319
energy:I(energy ** 3):playlist_subgenre[T.latin hip hop] -1.0843 1.007 -1.076 0.282 -3.059 0.890
energy:I(energy ** 3):playlist_subgenre[T.latin pop] 1.1458 0.839 1.366 0.172 -0.498 2.790
energy:I(energy ** 3):playlist_subgenre[T.neo soul] 0.4695 0.765 0.614 0.539 -1.029 1.968
energy:I(energy ** 3):playlist_subgenre[T.new jack swing] -0.1113 0.930 -0.120 0.905 -1.935 1.712
energy:I(energy ** 3):playlist_subgenre[T.permanent wave] 0.4380 0.751 0.583 0.560 -1.034 1.910
energy:I(energy ** 3):playlist_subgenre[T.pop edm] 0.4824 1.272 0.379 0.704 -2.010 2.975
energy:I(energy ** 3):playlist_subgenre[T.post-teen pop] 0.1193 0.821 0.145 0.884 -1.489 1.728
energy:I(energy ** 3):playlist_subgenre[T.progressive electro house] 0.9480 1.072 0.885 0.376 -1.152 3.048
energy:I(energy ** 3):playlist_subgenre[T.reggaeton] -5.5372 2.295 -2.412 0.016 -10.036 -1.038
energy:I(energy ** 3):playlist_subgenre[T.southern hip hop] 1.2382 1.097 1.129 0.259 -0.912 3.388
energy:I(energy ** 3):playlist_subgenre[T.trap] -0.3119 1.075 -0.290 0.772 -2.418 1.795
energy:I(energy ** 3):playlist_subgenre[T.tropical] 0.1457 0.776 0.188 0.851 -1.375 1.667
energy:I(energy ** 3):playlist_subgenre[T.urban contemporary] 0.0157 0.772 0.020 0.984 -1.497 1.528
I(energy ** 2):I(energy ** 3) -0.0199 0.092 -0.216 0.829 -0.201 0.161
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.big room] -0.5195 0.803 -0.647 0.518 -2.094 1.055
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.classic rock] -0.3620 0.206 -1.760 0.078 -0.765 0.041
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.dance pop] 0.2765 0.189 1.464 0.143 -0.094 0.647
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.electro house] 0.0037 0.193 0.019 0.985 -0.374 0.381
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.electropop] -0.1909 0.155 -1.231 0.218 -0.495 0.113
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.gangster rap] 0.4430 0.292 1.518 0.129 -0.129 1.015
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.hard rock] 0.2149 0.223 0.962 0.336 -0.223 0.653
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.hip hop] 0.1145 0.119 0.965 0.335 -0.118 0.347
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.hip pop] -0.0167 0.188 -0.089 0.929 -0.385 0.352
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.indie poptimism] 0.1170 0.126 0.926 0.354 -0.131 0.365
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.latin hip hop] -0.1489 0.236 -0.630 0.528 -0.612 0.314
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.latin pop] 0.2026 0.147 1.376 0.169 -0.086 0.491
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.neo soul] 0.0613 0.124 0.494 0.621 -0.182 0.304
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.new jack swing] 0.1060 0.187 0.567 0.570 -0.260 0.472
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.permanent wave] 0.0982 0.126 0.779 0.436 -0.149 0.345
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.pop edm] 0.1666 0.394 0.423 0.672 -0.606 0.939
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.post-teen pop] 0.0249 0.141 0.176 0.860 -0.251 0.301
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.progressive electro house] 0.7693 0.661 1.164 0.245 -0.526 2.065
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.reggaeton] -4.0745 1.770 -2.302 0.021 -7.545 -0.604
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.southern hip hop] 0.3327 0.300 1.109 0.267 -0.255 0.921
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.trap] -0.0260 0.277 -0.094 0.925 -0.570 0.518
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.tropical] 0.0487 0.126 0.386 0.700 -0.199 0.296
I(energy ** 2):I(energy ** 3):playlist_subgenre[T.urban contemporary] 0.0066 0.121 0.055 0.956 -0.230 0.243
valence:I(valence ** 2) -0.4365 0.780 -0.559 0.576 -1.966 1.093
valence:I(valence ** 2):playlist_subgenre[T.big room] 1.2427 1.083 1.148 0.251 -0.880 3.365
valence:I(valence ** 2):playlist_subgenre[T.classic rock] -0.4502 1.209 -0.373 0.709 -2.819 1.919
valence:I(valence ** 2):playlist_subgenre[T.dance pop] -0.7714 1.083 -0.712 0.476 -2.894 1.351
valence:I(valence ** 2):playlist_subgenre[T.electro house] -0.0741 0.980 -0.076 0.940 -1.995 1.847
valence:I(valence ** 2):playlist_subgenre[T.electropop] 0.0723 1.051 0.069 0.945 -1.988 2.133
valence:I(valence ** 2):playlist_subgenre[T.gangster rap] 0.0234 1.023 0.023 0.982 -1.982 2.029
valence:I(valence ** 2):playlist_subgenre[T.hard rock] 0.9972 1.129 0.883 0.377 -1.216 3.211
valence:I(valence ** 2):playlist_subgenre[T.hip hop] 1.8362 1.050 1.748 0.080 -0.222 3.895
valence:I(valence ** 2):playlist_subgenre[T.hip pop] 1.1960 1.204 0.994 0.320 -1.163 3.555
valence:I(valence ** 2):playlist_subgenre[T.indie poptimism] 0.3733 0.998 0.374 0.708 -1.583 2.329
valence:I(valence ** 2):playlist_subgenre[T.latin hip hop] 1.4700 1.186 1.239 0.215 -0.855 3.795
valence:I(valence ** 2):playlist_subgenre[T.latin pop] 0.6063 1.207 0.502 0.615 -1.760 2.973
valence:I(valence ** 2):playlist_subgenre[T.neo soul] -0.0436 1.056 -0.041 0.967 -2.114 2.026
valence:I(valence ** 2):playlist_subgenre[T.new jack swing] 1.6914 1.399 1.209 0.227 -1.051 4.434
valence:I(valence ** 2):playlist_subgenre[T.permanent wave] 1.0159 1.156 0.879 0.380 -1.250 3.282
valence:I(valence ** 2):playlist_subgenre[T.pop edm] 0.9962 1.113 0.895 0.371 -1.186 3.178
valence:I(valence ** 2):playlist_subgenre[T.post-teen pop] 0.0588 1.221 0.048 0.962 -2.335 2.452
valence:I(valence ** 2):playlist_subgenre[T.progressive electro house] 0.2106 0.963 0.219 0.827 -1.677 2.099
valence:I(valence ** 2):playlist_subgenre[T.reggaeton] -2.0878 1.896 -1.101 0.271 -5.804 1.629
valence:I(valence ** 2):playlist_subgenre[T.southern hip hop] 0.7320 1.056 0.693 0.488 -1.338 2.802
valence:I(valence ** 2):playlist_subgenre[T.trap] 0.8263 1.045 0.791 0.429 -1.222 2.875
valence:I(valence ** 2):playlist_subgenre[T.tropical] -1.2864 1.049 -1.226 0.220 -3.343 0.771
valence:I(valence ** 2):playlist_subgenre[T.urban contemporary] 1.3076 1.044 1.253 0.210 -0.738 3.353
valence:I(valence ** 3) -0.1137 0.548 -0.207 0.836 -1.188 0.961
valence:I(valence ** 3):playlist_subgenre[T.big room] 2.7449 1.426 1.925 0.054 -0.050 5.540
valence:I(valence ** 3):playlist_subgenre[T.classic rock] -0.2669 0.741 -0.360 0.719 -1.720 1.186
valence:I(valence ** 3):playlist_subgenre[T.dance pop] 0.5614 0.771 0.728 0.466 -0.950 2.072
valence:I(valence ** 3):playlist_subgenre[T.electro house] 0.6695 0.790 0.847 0.397 -0.879 2.218
valence:I(valence ** 3):playlist_subgenre[T.electropop] -0.0683 0.754 -0.091 0.928 -1.546 1.409
valence:I(valence ** 3):playlist_subgenre[T.gangster rap] 1.1263 0.806 1.397 0.163 -0.454 2.707
valence:I(valence ** 3):playlist_subgenre[T.hard rock] -0.7062 0.860 -0.822 0.411 -2.391 0.979
valence:I(valence ** 3):playlist_subgenre[T.hip hop] -0.2267 0.771 -0.294 0.769 -1.738 1.285
valence:I(valence ** 3):playlist_subgenre[T.hip pop] 0.3944 0.873 0.452 0.652 -1.318 2.106
valence:I(valence ** 3):playlist_subgenre[T.indie poptimism] 0.5468 0.792 0.691 0.490 -1.005 2.099
valence:I(valence ** 3):playlist_subgenre[T.latin hip hop] -0.4390 0.731 -0.601 0.548 -1.871 0.993
valence:I(valence ** 3):playlist_subgenre[T.latin pop] 0.0181 0.736 0.025 0.980 -1.425 1.461
valence:I(valence ** 3):playlist_subgenre[T.neo soul] -0.2401 0.751 -0.320 0.749 -1.712 1.232
valence:I(valence ** 3):playlist_subgenre[T.new jack swing] -0.2876 0.800 -0.359 0.719 -1.856 1.281
valence:I(valence ** 3):playlist_subgenre[T.permanent wave] -0.3514 0.773 -0.454 0.649 -1.867 1.164
valence:I(valence ** 3):playlist_subgenre[T.pop edm] -0.0179 0.876 -0.020 0.984 -1.735 1.699
valence:I(valence ** 3):playlist_subgenre[T.post-teen pop] 0.5031 0.794 0.634 0.526 -1.053 2.059
valence:I(valence ** 3):playlist_subgenre[T.progressive electro house] 0.1620 0.786 0.206 0.837 -1.380 1.703
valence:I(valence ** 3):playlist_subgenre[T.reggaeton] -2.1601 1.177 -1.835 0.067 -4.468 0.148
valence:I(valence ** 3):playlist_subgenre[T.southern hip hop] 0.1527 0.730 0.209 0.834 -1.278 1.583
valence:I(valence ** 3):playlist_subgenre[T.trap] 1.4775 0.880 1.679 0.093 -0.247 3.202
valence:I(valence ** 3):playlist_subgenre[T.tropical] 0.5104 0.750 0.681 0.496 -0.959 1.980
valence:I(valence ** 3):playlist_subgenre[T.urban contemporary] -0.2287 0.768 -0.298 0.766 -1.734 1.277
I(valence ** 2):I(valence ** 3) 0.1119 0.373 0.300 0.764 -0.620 0.844
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.big room] 0.7091 0.622 1.139 0.255 -0.511 1.929
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.classic rock] 0.3554 0.578 0.615 0.539 -0.778 1.489
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.dance pop] 0.4603 0.531 0.867 0.386 -0.580 1.501
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.electro house] 0.1278 0.482 0.265 0.791 -0.816 1.072
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.electropop] 0.0242 0.507 0.048 0.962 -0.969 1.018
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.gangster rap] 0.1846 0.504 0.367 0.714 -0.802 1.172
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.hard rock] -0.5065 0.577 -0.877 0.380 -1.638 0.625
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.hip hop] -0.6023 0.512 -1.177 0.239 -1.606 0.401
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.hip pop] -0.3335 0.591 -0.564 0.572 -1.492 0.825
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.indie poptimism] 0.0988 0.499 0.198 0.843 -0.880 1.078
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.latin hip hop] -0.7236 0.559 -1.295 0.195 -1.819 0.372
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.latin pop] -0.2676 0.572 -0.468 0.640 -1.389 0.854
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.neo soul] -0.0121 0.519 -0.023 0.981 -1.030 1.006
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.new jack swing] -0.4331 0.667 -0.649 0.516 -1.740 0.874
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.permanent wave] -0.3998 0.549 -0.728 0.466 -1.476 0.676
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.pop edm] -0.2292 0.553 -0.415 0.678 -1.313 0.854
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.post-teen pop] 0.3031 0.598 0.507 0.612 -0.868 1.475
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.progressive electro house] -0.0968 0.472 -0.205 0.837 -1.021 0.828
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.reggaeton] 1.2649 1.039 1.217 0.224 -0.772 3.302
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.southern hip hop] -0.1865 0.513 -0.364 0.716 -1.192 0.819
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.trap] 0.1868 0.530 0.353 0.724 -0.851 1.225
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.tropical] 0.5160 0.498 1.036 0.300 -0.460 1.492
I(valence ** 2):I(valence ** 3):playlist_subgenre[T.urban contemporary] -0.4358 0.502 -0.868 0.385 -1.420 0.548
tempo:I(tempo ** 2) 0.0515 0.125 0.411 0.681 -0.194 0.297
tempo:I(tempo ** 2):playlist_subgenre[T.big room] -0.3281 1.241 -0.264 0.792 -2.761 2.105
tempo:I(tempo ** 2):playlist_subgenre[T.classic rock] -0.3419 0.315 -1.087 0.277 -0.959 0.275
tempo:I(tempo ** 2):playlist_subgenre[T.dance pop] -0.0782 0.358 -0.219 0.827 -0.779 0.623
tempo:I(tempo ** 2):playlist_subgenre[T.electro house] -0.0251 0.783 -0.032 0.974 -1.561 1.510
tempo:I(tempo ** 2):playlist_subgenre[T.electropop] -0.3229 0.478 -0.675 0.500 -1.260 0.614
tempo:I(tempo ** 2):playlist_subgenre[T.gangster rap] -0.2686 0.314 -0.855 0.393 -0.884 0.347
tempo:I(tempo ** 2):playlist_subgenre[T.hard rock] -0.4763 0.490 -0.973 0.331 -1.436 0.483
tempo:I(tempo ** 2):playlist_subgenre[T.hip hop] -0.0762 0.196 -0.388 0.698 -0.461 0.309
tempo:I(tempo ** 2):playlist_subgenre[T.hip pop] 0.3039 0.333 0.913 0.361 -0.348 0.956
tempo:I(tempo ** 2):playlist_subgenre[T.indie poptimism] -0.5295 0.365 -1.450 0.147 -1.245 0.186
tempo:I(tempo ** 2):playlist_subgenre[T.latin hip hop] 0.1006 0.322 0.313 0.754 -0.530 0.731
tempo:I(tempo ** 2):playlist_subgenre[T.latin pop] -0.2120 0.442 -0.479 0.632 -1.079 0.655
tempo:I(tempo ** 2):playlist_subgenre[T.neo soul] -0.0467 0.224 -0.209 0.835 -0.485 0.392
tempo:I(tempo ** 2):playlist_subgenre[T.new jack swing] 0.1271 0.518 0.245 0.806 -0.889 1.143
tempo:I(tempo ** 2):playlist_subgenre[T.permanent wave] -0.1062 0.278 -0.382 0.702 -0.650 0.438
tempo:I(tempo ** 2):playlist_subgenre[T.pop edm] -0.0419 0.530 -0.079 0.937 -1.081 0.997
tempo:I(tempo ** 2):playlist_subgenre[T.post-teen pop] 0.0994 0.460 0.216 0.829 -0.802 1.001
tempo:I(tempo ** 2):playlist_subgenre[T.progressive electro house] 0.0730 1.332 0.055 0.956 -2.539 2.684
tempo:I(tempo ** 2):playlist_subgenre[T.reggaeton] -0.7172 0.649 -1.106 0.269 -1.989 0.554
tempo:I(tempo ** 2):playlist_subgenre[T.southern hip hop] -0.1978 0.282 -0.702 0.483 -0.751 0.355
tempo:I(tempo ** 2):playlist_subgenre[T.trap] 0.7734 0.654 1.183 0.237 -0.508 2.055
tempo:I(tempo ** 2):playlist_subgenre[T.tropical] -0.7687 0.528 -1.455 0.146 -1.804 0.267
tempo:I(tempo ** 2):playlist_subgenre[T.urban contemporary] 0.1227 0.358 0.343 0.732 -0.580 0.825
tempo:I(tempo ** 3) 0.2347 0.171 1.375 0.169 -0.100 0.569
tempo:I(tempo ** 3):playlist_subgenre[T.big room] -0.4131 0.512 -0.807 0.420 -1.417 0.591
tempo:I(tempo ** 3):playlist_subgenre[T.classic rock] -0.1490 0.256 -0.581 0.561 -0.652 0.354
tempo:I(tempo ** 3):playlist_subgenre[T.dance pop] -0.3810 0.307 -1.240 0.215 -0.983 0.221
tempo:I(tempo ** 3):playlist_subgenre[T.electro house] -0.3815 0.347 -1.100 0.271 -1.061 0.298
tempo:I(tempo ** 3):playlist_subgenre[T.electropop] -0.6412 0.274 -2.340 0.019 -1.178 -0.104
tempo:I(tempo ** 3):playlist_subgenre[T.gangster rap] -0.2395 0.260 -0.923 0.356 -0.749 0.269
tempo:I(tempo ** 3):playlist_subgenre[T.hard rock] -0.5725 0.281 -2.035 0.042 -1.124 -0.021
tempo:I(tempo ** 3):playlist_subgenre[T.hip hop] -0.1286 0.235 -0.547 0.585 -0.590 0.333
tempo:I(tempo ** 3):playlist_subgenre[T.hip pop] -0.4522 0.280 -1.614 0.107 -1.001 0.097
tempo:I(tempo ** 3):playlist_subgenre[T.indie poptimism] 0.2957 0.244 1.211 0.226 -0.183 0.774
tempo:I(tempo ** 3):playlist_subgenre[T.latin hip hop] -0.1470 0.211 -0.697 0.486 -0.560 0.266
tempo:I(tempo ** 3):playlist_subgenre[T.latin pop] -0.4544 0.255 -1.783 0.075 -0.954 0.045
tempo:I(tempo ** 3):playlist_subgenre[T.neo soul] -0.3703 0.235 -1.578 0.115 -0.830 0.090
tempo:I(tempo ** 3):playlist_subgenre[T.new jack swing] -0.2693 0.263 -1.024 0.306 -0.785 0.246
tempo:I(tempo ** 3):playlist_subgenre[T.permanent wave] -0.2888 0.262 -1.102 0.271 -0.803 0.225
tempo:I(tempo ** 3):playlist_subgenre[T.pop edm] -0.1193 0.310 -0.385 0.700 -0.727 0.488
tempo:I(tempo ** 3):playlist_subgenre[T.post-teen pop] -0.7607 0.281 -2.705 0.007 -1.312 -0.209
tempo:I(tempo ** 3):playlist_subgenre[T.progressive electro house] -0.2251 0.735 -0.306 0.759 -1.666 1.216
tempo:I(tempo ** 3):playlist_subgenre[T.reggaeton] -0.0292 0.296 -0.099 0.921 -0.609 0.551
tempo:I(tempo ** 3):playlist_subgenre[T.southern hip hop] 0.2172 0.233 0.930 0.352 -0.240 0.675
tempo:I(tempo ** 3):playlist_subgenre[T.trap] -0.1845 0.367 -0.503 0.615 -0.904 0.535
tempo:I(tempo ** 3):playlist_subgenre[T.tropical] 0.0844 0.329 0.257 0.798 -0.560 0.729
tempo:I(tempo ** 3):playlist_subgenre[T.urban contemporary] -0.0559 0.245 -0.228 0.820 -0.536 0.424
I(tempo ** 2):I(tempo ** 3) 0.0125 0.008 1.541 0.123 -0.003 0.028
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.big room] 0.1114 0.429 0.259 0.795 -0.730 0.953
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.classic rock] 0.0703 0.069 1.012 0.312 -0.066 0.207
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.dance pop] -0.0354 0.087 -0.406 0.685 -0.206 0.135
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.electro house] -0.0301 0.202 -0.149 0.881 -0.426 0.365
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.electropop] 0.0908 0.139 0.651 0.515 -0.182 0.364
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.gangster rap] 0.0294 0.075 0.391 0.696 -0.118 0.177
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.hard rock] 0.1041 0.159 0.655 0.512 -0.207 0.416
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.hip hop] 0.0095 0.035 0.270 0.787 -0.059 0.078
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.hip pop] -0.1042 0.074 -1.414 0.157 -0.249 0.040
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.indie poptimism] 0.1657 0.102 1.628 0.104 -0.034 0.365
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.latin hip hop] -0.0473 0.052 -0.902 0.367 -0.150 0.056
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.latin pop] 0.0035 0.119 0.029 0.977 -0.230 0.237
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.neo soul] -0.0289 0.046 -0.624 0.533 -0.120 0.062
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.new jack swing] -0.0277 0.138 -0.201 0.841 -0.298 0.242
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.permanent wave] -0.0096 0.047 -0.204 0.838 -0.101 0.082
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.pop edm] -0.0355 0.152 -0.233 0.815 -0.334 0.263
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.post-teen pop] -0.1161 0.135 -0.861 0.389 -0.381 0.148
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.progressive electro house] -0.2423 0.535 -0.453 0.650 -1.290 0.806
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.reggaeton] 0.0486 0.152 0.320 0.749 -0.249 0.347
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.southern hip hop] 0.0676 0.065 1.043 0.297 -0.059 0.195
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.trap] -0.3743 0.249 -1.502 0.133 -0.863 0.114
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.tropical] 0.2036 0.163 1.247 0.212 -0.116 0.524
I(tempo ** 2):I(tempo ** 3):playlist_subgenre[T.urban contemporary] -0.0446 0.094 -0.473 0.636 -0.230 0.140
duration_ms:I(duration_ms ** 2) 0.1896 0.105 1.811 0.070 -0.016 0.395
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.big room] -0.1102 0.711 -0.155 0.877 -1.503 1.283
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.classic rock] -0.4854 0.322 -1.509 0.131 -1.116 0.145
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.dance pop] -0.1882 0.504 -0.373 0.709 -1.177 0.801
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.electro house] -0.1405 0.120 -1.168 0.243 -0.376 0.095
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.electropop] 0.3583 0.292 1.226 0.220 -0.215 0.931
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.gangster rap] -0.3174 0.213 -1.490 0.136 -0.735 0.100
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.hard rock] -0.1468 0.309 -0.475 0.635 -0.753 0.459
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.hip hop] -0.1190 0.174 -0.685 0.493 -0.460 0.222
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.hip pop] -0.2361 0.220 -1.073 0.283 -0.667 0.195
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.indie poptimism] -0.3843 0.492 -0.781 0.435 -1.349 0.580
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.latin hip hop] -0.2322 0.207 -1.123 0.262 -0.637 0.173
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.latin pop] -0.2180 0.365 -0.597 0.550 -0.934 0.498
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.neo soul] -0.4898 0.221 -2.213 0.027 -0.924 -0.056
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.new jack swing] -0.4285 0.188 -2.278 0.023 -0.797 -0.060
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.permanent wave] 0.2006 0.428 0.469 0.639 -0.638 1.039
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.pop edm] -0.6275 0.561 -1.119 0.263 -1.727 0.472
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.post-teen pop] -0.6304 0.268 -2.356 0.018 -1.155 -0.106
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.progressive electro house] 0.0054 0.283 0.019 0.985 -0.549 0.560
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.reggaeton] 0.3751 0.583 0.643 0.520 -0.767 1.518
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.southern hip hop] -0.2811 0.122 -2.295 0.022 -0.521 -0.041
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.trap] 0.1298 0.412 0.315 0.753 -0.678 0.937
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.tropical] -0.2456 0.188 -1.308 0.191 -0.614 0.123
duration_ms:I(duration_ms ** 2):playlist_subgenre[T.urban contemporary] -0.5350 0.218 -2.459 0.014 -0.961 -0.109
duration_ms:I(duration_ms ** 3) -0.0175 0.061 -0.286 0.775 -0.138 0.103
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.big room] 0.2683 0.375 0.715 0.475 -0.467 1.004
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.classic rock] -0.2771 0.187 -1.482 0.138 -0.644 0.089
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.dance pop] 0.0822 0.214 0.383 0.702 -0.338 0.503
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.electro house] 0.0302 0.081 0.374 0.708 -0.128 0.189
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.electropop] -0.0070 0.115 -0.061 0.951 -0.232 0.218
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.gangster rap] 0.1691 0.187 0.906 0.365 -0.197 0.535
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.hard rock] -0.0600 0.108 -0.556 0.578 -0.272 0.152
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.hip hop] 0.1048 0.159 0.658 0.511 -0.207 0.417
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.hip pop] -0.1977 0.211 -0.936 0.349 -0.612 0.216
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.indie poptimism] 0.4215 0.253 1.666 0.096 -0.074 0.917
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.latin hip hop] -0.0207 0.102 -0.203 0.839 -0.221 0.179
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.latin pop] -0.2242 0.301 -0.744 0.457 -0.815 0.367
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.neo soul] -0.0259 0.102 -0.254 0.800 -0.226 0.174
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.new jack swing] 0.1092 0.143 0.765 0.445 -0.171 0.389
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.permanent wave] -0.0732 0.231 -0.318 0.751 -0.525 0.379
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.pop edm] 0.1402 0.242 0.580 0.562 -0.334 0.614
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.post-teen pop] -0.4912 0.260 -1.891 0.059 -1.000 0.018
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.progressive electro house] -0.0996 0.333 -0.299 0.765 -0.753 0.554
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.reggaeton] 0.0351 0.196 0.179 0.858 -0.348 0.419
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.southern hip hop] -0.0830 0.083 -0.996 0.319 -0.246 0.080
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.trap] -0.2309 0.194 -1.192 0.233 -0.610 0.149
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.tropical] -0.1163 0.189 -0.614 0.539 -0.487 0.255
duration_ms:I(duration_ms ** 3):playlist_subgenre[T.urban contemporary] 0.0156 0.111 0.140 0.888 -0.202 0.233
I(duration_ms ** 2):I(duration_ms ** 3) -0.0140 0.014 -1.032 0.302 -0.041 0.013
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.big room] 0.0049 0.280 0.018 0.986 -0.545 0.555
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.classic rock] 0.1171 0.075 1.568 0.117 -0.029 0.264
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.dance pop] 0.0331 0.129 0.257 0.797 -0.219 0.285
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.electro house] 0.0144 0.015 0.968 0.333 -0.015 0.044
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.electropop] -0.0736 0.049 -1.516 0.130 -0.169 0.022
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.gangster rap] 0.0704 0.049 1.421 0.155 -0.027 0.167
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.hard rock] -0.0023 0.047 -0.049 0.961 -0.095 0.091
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.hip hop] 0.0303 0.025 1.205 0.228 -0.019 0.080
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.hip pop] -0.0192 0.041 -0.465 0.642 -0.100 0.062
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.indie poptimism] 0.0225 0.152 0.148 0.883 -0.276 0.321
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.latin hip hop] 0.0158 0.029 0.545 0.586 -0.041 0.073
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.latin pop] -0.0120 0.080 -0.151 0.880 -0.168 0.144
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.neo soul] 0.0513 0.036 1.439 0.150 -0.019 0.121
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.new jack swing] 0.0316 0.023 1.355 0.176 -0.014 0.077
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.permanent wave] -0.0897 0.114 -0.784 0.433 -0.314 0.135
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.pop edm] 0.1411 0.157 0.899 0.368 -0.166 0.449
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.post-teen pop] -0.0364 0.032 -1.124 0.261 -0.100 0.027
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.progressive electro house] 0.0242 0.099 0.245 0.807 -0.170 0.219
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.reggaeton] -0.0469 0.121 -0.388 0.698 -0.284 0.190
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.southern hip hop] 0.0059 0.015 0.391 0.696 -0.024 0.035
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.trap] 0.0137 0.109 0.126 0.899 -0.199 0.226
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.tropical] -0.0035 0.027 -0.132 0.895 -0.056 0.049
I(duration_ms ** 2):I(duration_ms ** 3):playlist_subgenre[T.urban contemporary] 0.0518 0.032 1.622 0.105 -0.011 0.115
artist_hit_rate:I(artist_hit_rate ** 2) 3.2005 2.885 1.109 0.267 -2.454 8.855
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.big room] -4.7891 8.628 -0.555 0.579 -21.700 12.121
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.classic rock] -10.0471 4.020 -2.499 0.012 -17.927 -2.168
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.dance pop] 2.2625 3.708 0.610 0.542 -5.005 9.530
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.electro house] 14.4122 7.847 1.837 0.066 -0.969 29.793
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.electropop] -0.3761 3.598 -0.105 0.917 -7.429 6.677
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.gangster rap] -3.7236 3.678 -1.012 0.311 -10.933 3.486
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.hard rock] -0.7139 4.116 -0.173 0.862 -8.781 7.353
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.hip hop] -6.2794 3.910 -1.606 0.108 -13.943 1.384
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.hip pop] -5.1457 4.507 -1.142 0.254 -13.979 3.688
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.indie poptimism] -10.3522 4.116 -2.515 0.012 -18.419 -2.285
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.latin hip hop] -3.7359 4.000 -0.934 0.350 -11.577 4.105
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.latin pop] -2.9068 3.804 -0.764 0.445 -10.362 4.548
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.neo soul] -6.0084 4.542 -1.323 0.186 -14.912 2.895
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.new jack swing] -6.4789 17.730 -0.365 0.715 -41.230 28.272
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.permanent wave] 2.5716 3.938 0.653 0.514 -5.147 10.290
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.pop edm] -1.0555 4.403 -0.240 0.811 -9.686 7.575
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.post-teen pop] -2.4475 3.617 -0.677 0.499 -9.538 4.643
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.progressive electro house] -5.9912 7.550 -0.794 0.427 -20.789 8.806
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.reggaeton] -2.8819 3.729 -0.773 0.440 -10.191 4.428
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.southern hip hop] 7.5348 4.543 1.659 0.097 -1.369 16.439
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.trap] -5.0470 3.710 -1.360 0.174 -12.318 2.224
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.tropical] -11.3145 4.720 -2.397 0.017 -20.565 -2.064
artist_hit_rate:I(artist_hit_rate ** 2):playlist_subgenre[T.urban contemporary] -1.2146 3.830 -0.317 0.751 -8.721 6.292
artist_hit_rate:I(artist_hit_rate ** 3) -2.1489 2.100 -1.023 0.306 -6.265 1.967
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.big room] 3.3750 9.631 0.350 0.726 -15.501 22.251
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.classic rock] 7.3700 3.033 2.430 0.015 1.425 13.315
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.dance pop] -1.2555 2.591 -0.485 0.628 -6.334 3.823
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.electro house] -13.9100 7.205 -1.931 0.054 -28.032 0.212
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.electropop] 0.0341 2.540 0.013 0.989 -4.945 5.013
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.gangster rap] 2.7191 2.635 1.032 0.302 -2.446 7.885
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.hard rock] 0.8815 3.039 0.290 0.772 -5.075 6.838
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.hip hop] 4.5734 2.641 1.732 0.083 -0.602 9.749
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.hip pop] 2.9981 3.022 0.992 0.321 -2.925 8.921
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.indie poptimism] 6.5831 2.864 2.298 0.022 0.969 12.198
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.latin hip hop] 1.9190 2.799 0.686 0.493 -3.568 7.406
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.latin pop] 2.0069 2.610 0.769 0.442 -3.108 7.122
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.neo soul] 3.7036 3.334 1.111 0.267 -2.831 10.238
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.new jack swing] 11.6284 77.192 0.151 0.880 -139.672 162.928
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.permanent wave] -0.8448 2.719 -0.311 0.756 -6.174 4.484
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.pop edm] 1.3123 3.083 0.426 0.670 -4.731 7.356
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.post-teen pop] 2.1370 2.505 0.853 0.394 -2.773 7.047
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.progressive electro house] 3.8162 8.628 0.442 0.658 -13.094 20.727
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.reggaeton] 1.8413 2.631 0.700 0.484 -3.316 6.998
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.southern hip hop] -8.0530 3.859 -2.087 0.037 -15.617 -0.489
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.trap] 3.7038 2.579 1.436 0.151 -1.352 8.759
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.tropical] 8.4015 3.348 2.509 0.012 1.839 14.964
artist_hit_rate:I(artist_hit_rate ** 3):playlist_subgenre[T.urban contemporary] 1.3441 2.610 0.515 0.607 -3.771 6.459
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3) 0.2181 0.234 0.931 0.352 -0.241 0.677
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.big room] -0.2728 1.587 -0.172 0.864 -3.384 2.839
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.classic rock] -0.8068 0.348 -2.317 0.020 -1.489 -0.124
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.dance pop] 0.1271 0.283 0.449 0.654 -0.428 0.682
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.electro house] 2.0113 1.014 1.983 0.047 0.023 3.999
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.electropop] 0.0073 0.279 0.026 0.979 -0.540 0.554
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.gangster rap] -0.2957 0.291 -1.016 0.310 -0.866 0.275
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.hard rock] -0.1196 0.341 -0.350 0.726 -0.789 0.550
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.hip hop] -0.4936 0.283 -1.744 0.081 -1.048 0.061
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.hip pop] -0.2749 0.322 -0.855 0.392 -0.905 0.355
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.indie poptimism] -0.6438 0.313 -2.058 0.040 -1.257 -0.031
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.latin hip hop] -0.1567 0.306 -0.511 0.609 -0.757 0.444
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.latin pop] -0.2100 0.282 -0.745 0.456 -0.762 0.342
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.neo soul] -0.3653 0.374 -0.977 0.329 -1.098 0.368
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.new jack swing] -7.1734 31.250 -0.230 0.818 -68.426 54.079
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.permanent wave] 0.0478 0.295 0.162 0.871 -0.530 0.626
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.pop edm] -0.1720 0.337 -0.511 0.609 -0.832 0.488
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.post-teen pop] -0.2412 0.273 -0.884 0.377 -0.776 0.294
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.progressive electro house] -0.4461 1.453 -0.307 0.759 -3.294 2.402
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.reggaeton] -0.1785 0.289 -0.618 0.537 -0.745 0.388
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.southern hip hop] 1.1793 0.509 2.318 0.020 0.182 2.176
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.trap] -0.3981 0.281 -1.416 0.157 -0.949 0.153
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.tropical] -0.9223 0.369 -2.496 0.013 -1.647 -0.198
I(artist_hit_rate ** 2):I(artist_hit_rate ** 3):playlist_subgenre[T.urban contemporary] -0.1595 0.282 -0.567 0.571 -0.711 0.392
artist_n_tracks:I(artist_n_tracks ** 2) -1.2427 0.584 -2.128 0.033 -2.387 -0.098
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.big room] -0.2866 0.918 -0.312 0.755 -2.085 1.512
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.classic rock] -0.7137 0.827 -0.863 0.388 -2.334 0.907
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.dance pop] 0.7758 0.817 0.950 0.342 -0.825 2.376
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.electro house] 1.0229 0.881 1.162 0.245 -0.703 2.749
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.electropop] 1.6680 0.802 2.079 0.038 0.096 3.240
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.gangster rap] 1.1926 1.049 1.137 0.256 -0.864 3.249
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.hard rock] 1.0827 0.825 1.313 0.189 -0.533 2.699
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.hip hop] 1.7451 1.230 1.419 0.156 -0.666 4.156
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.hip pop] -1.3331 1.555 -0.857 0.391 -4.380 1.714
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.indie poptimism] 3.7295 1.187 3.141 0.002 1.402 6.057
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.latin hip hop] 3.2381 0.897 3.610 0.000 1.480 4.996
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.latin pop] 0.5250 0.976 0.538 0.590 -1.387 2.437
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.neo soul] 1.7630 1.597 1.104 0.270 -1.367 4.893
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.new jack swing] 0.2024 1.433 0.141 0.888 -2.607 3.012
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.permanent wave] 1.3165 0.948 1.389 0.165 -0.541 3.174
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.pop edm] 1.0125 0.935 1.084 0.279 -0.819 2.844
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.post-teen pop] 1.2006 0.842 1.426 0.154 -0.450 2.851
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.progressive electro house] 1.8730 0.827 2.265 0.024 0.252 3.494
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.reggaeton] 1.3049 0.991 1.316 0.188 -0.638 3.248
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.southern hip hop] 1.4305 0.841 1.701 0.089 -0.217 3.078
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.trap] 0.6050 1.173 0.516 0.606 -1.694 2.904
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.tropical] 0.6685 1.385 0.483 0.629 -2.046 3.383
artist_n_tracks:I(artist_n_tracks ** 2):playlist_subgenre[T.urban contemporary] 1.5519 1.042 1.489 0.136 -0.491 3.595
artist_n_tracks:I(artist_n_tracks ** 3) 3.6045 1.598 2.255 0.024 0.472 6.737
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.big room] -4.1255 2.452 -1.683 0.092 -8.931 0.680
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.classic rock] -6.9968 2.297 -3.047 0.002 -11.498 -2.495
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.dance pop] -3.3193 2.221 -1.494 0.135 -7.673 1.034
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.electro house] -4.4930 2.267 -1.982 0.047 -8.936 -0.050
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.electropop] -2.9992 2.168 -1.383 0.167 -7.249 1.250
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.gangster rap] -3.7405 2.516 -1.486 0.137 -8.673 1.192
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.hard rock] -2.2920 2.229 -1.028 0.304 -6.662 2.078
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.hip hop] -2.2987 2.515 -0.914 0.361 -7.227 2.630
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.hip pop] -6.9500 2.937 -2.366 0.018 -12.708 -1.193
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.indie poptimism] -1.7469 2.371 -0.737 0.461 -6.394 2.901
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.latin hip hop] -3.2219 2.346 -1.374 0.170 -7.820 1.376
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.latin pop] -4.5384 2.492 -1.821 0.069 -9.423 0.347
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.neo soul] -2.8045 2.550 -1.100 0.271 -7.803 2.194
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.new jack swing] -4.6840 3.148 -1.488 0.137 -10.854 1.486
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.permanent wave] -3.6405 2.516 -1.447 0.148 -8.572 1.291
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.pop edm] -6.0818 2.449 -2.483 0.013 -10.882 -1.282
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.post-teen pop] -4.3225 2.268 -1.906 0.057 -8.768 0.123
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.progressive electro house] -2.2684 2.210 -1.026 0.305 -6.601 2.064
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.reggaeton] -4.9152 2.809 -1.750 0.080 -10.421 0.591
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.southern hip hop] -1.5593 2.206 -0.707 0.480 -5.884 2.765
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.trap] -4.9515 2.509 -1.974 0.048 -9.869 -0.034
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.tropical] -4.2637 2.665 -1.600 0.110 -9.488 0.960
artist_n_tracks:I(artist_n_tracks ** 3):playlist_subgenre[T.urban contemporary] -3.6677 2.462 -1.490 0.136 -8.493 1.158
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3) -0.7902 0.411 -1.923 0.055 -1.596 0.015
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.big room] 1.3413 0.777 1.725 0.085 -0.183 2.865
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.classic rock] 2.1208 0.630 3.369 0.001 0.887 3.355
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.dance pop] 0.7739 0.669 1.156 0.248 -0.538 2.086
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.electro house] 1.2556 0.719 1.747 0.081 -0.153 2.664
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.electropop] 0.6012 0.623 0.964 0.335 -0.621 1.823
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.gangster rap] 0.7290 0.962 0.758 0.449 -1.157 2.615
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.hard rock] 0.3877 0.629 0.617 0.538 -0.845 1.620
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.hip hop] 0.1114 0.997 0.112 0.911 -1.843 2.066
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.hip pop] 2.4837 1.279 1.942 0.052 -0.023 4.990
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.indie poptimism] -1.1176 0.959 -1.166 0.244 -2.996 0.761
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.latin hip hop] 0.0719 0.747 0.096 0.923 -1.392 1.536
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.latin pop] 1.4012 0.838 1.673 0.094 -0.241 3.043
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.neo soul] -0.3598 1.455 -0.247 0.805 -3.211 2.492
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.new jack swing] 1.5646 1.455 1.075 0.282 -1.288 4.417
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.permanent wave] 0.8972 0.750 1.196 0.232 -0.573 2.367
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.pop edm] 1.7707 0.786 2.254 0.024 0.231 3.310
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.post-teen pop] 1.1527 0.652 1.768 0.077 -0.125 2.430
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.progressive electro house] 0.2297 0.679 0.338 0.735 -1.102 1.561
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.reggaeton] 1.2051 0.852 1.414 0.157 -0.465 2.875
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.southern hip hop] -0.0603 0.710 -0.085 0.932 -1.452 1.331
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.trap] 1.1968 0.994 1.204 0.229 -0.752 3.145
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.tropical] 1.0710 1.177 0.910 0.363 -1.236 3.378
I(artist_n_tracks ** 2):I(artist_n_tracks ** 3):playlist_subgenre[T.urban contemporary] 0.5905 0.906 0.652 0.515 -1.186 2.367
==============================================================================
Omnibus: 1798.596 Durbin-Watson: 1.765
Prob(Omnibus): 0.000 Jarque-Bera (JB): 4029.466
Skew: -0.413 Prob(JB): 0.00
Kurtosis: 4.652 Cond. No. 2.45e+19
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 3.64e-26. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.
m_8.params.size
1320
m_8.params[m_8.pvalues < 0.05].size
103
m_8.params[m_8.pvalues < 0.05].sort_values(key=abs,ascending=False)
Intercept 29.769541
I(playlist_avg_popularity ** 2):playlist_subgenre[T.permanent wave] -20.893496
artist_avg_popularity 19.736311
I(playlist_avg_popularity ** 2):playlist_subgenre[T.dance pop] -15.460021
I(artist_hit_rate ** 2):playlist_subgenre[T.new jack swing] 14.905346
...
I(artist_avg_popularity ** 3):I(artist_n_tracks ** 3) 0.070034
I(playlist_avg_popularity ** 3):I(artist_n_tracks ** 3) -0.063329
I(playlist_avg_popularity ** 3):I(artist_hit_rate ** 3) -0.035294
I(artist_avg_popularity ** 3):I(playlist_avg_popularity ** 3) -0.009261
I(playlist_avg_popularity ** 3):I(tempo ** 3) 0.009132
Length: 103, dtype: float64
m_8.params[m_8.pvalues < 0.05].sort_values(key=abs,ascending=False)[1:3]
I(playlist_avg_popularity ** 2):playlist_subgenre[T.permanent wave] -20.893496 artist_avg_popularity 19.736311 dtype: float64
print(f'R squared: {m_8.rsquared}, RMSE: {m_8.mse_resid**0.5}')
R squared: 0.6473235894945797, RMSE: 14.271722969518153
viz_fitted_vs_actual(m_8.fittedvalues, spotify_model['track_popularity'], 'Most Complex Model')
Best performing model and most complex one. This might come with trade off of out of sample performance.
Prediction¶
You must predict with the model with ALL inputs and linear additive features.
This corresponds to model 4
f_4
'track_popularity ~ danceability + energy + speechiness + acousticness + instrumentalness + liveness + valence + tempo + duration_ms + artist_avg_popularity + artist_hit_rate + artist_n_tracks + artist_energy_mean + artist_danceability_mean + artist_valence_mean + artist_tempo_mean + artist_acousticness_mean + artist_speechiness_mean + artist_instrumentalness_mean + artist_liveness_mean+ playlist_avg_popularity + playlist_subgenre + mode + artist_n_genres + key'
You must identify the continuous input that you feel is the MOST important based on the statistically significant coefficients in your models.
The most important variable in all models is artist_avg_popularity.
The MOST important input must have 101 unique values between the minimum and maximum training set values.
m_4.params[m_4.pvalues < 0.05].sort_values(key=abs,ascending=False)
Intercept 41.847548 artist_avg_popularity 12.773867 playlist_subgenre[T.new jack swing] -9.898682 playlist_subgenre[T.progressive electro house] -8.117527 playlist_subgenre[T.big room] -7.707655 playlist_subgenre[T.gangster rap] -7.379152 playlist_subgenre[T.hard rock] -7.049828 playlist_subgenre[T.post-teen pop] 5.741450 playlist_subgenre[T.pop edm] -5.734722 playlist_subgenre[T.neo soul] -5.416762 playlist_subgenre[T.electro house] -5.350412 playlist_subgenre[T.permanent wave] 5.197357 playlist_subgenre[T.southern hip hop] -5.132238 playlist_subgenre[T.dance pop] 4.624844 artist_hit_rate 4.414877 playlist_subgenre[T.latin hip hop] -3.553230 artist_n_genres[T.5] -3.499970 playlist_subgenre[T.hip hop] 3.331415 playlist_subgenre[T.classic rock] -3.144928 playlist_subgenre[T.tropical] -2.329610 playlist_subgenre[T.indie poptimism] -2.069192 playlist_subgenre[T.electropop] -1.467199 instrumentalness -1.425685 artist_n_tracks -1.373468 energy -1.264087 artist_energy_mean 1.136957 artist_instrumentalness_mean 0.981730 artist_valence_mean -0.819208 artist_n_genres[T.2] -0.676694 danceability 0.652449 artist_speechiness_mean 0.605856 valence 0.552617 duration_ms -0.415607 speechiness -0.405382 dtype: float64
viz_1 = pd.DataFrame({'artist_avg_popularity':np.linspace(np.min(spotify_model['artist_avg_popularity']), np.max(spotify_model['artist_avg_popularity']), 101)})
viz_1['playlist_avg_popularity'] = np.mean(spotify_model['playlist_avg_popularity'])
viz_1['danceability'] = np.mean(spotify_model['danceability'])
viz_1['energy'] = np.mean(spotify_model['energy'])
viz_1['speechiness'] = np.mean(spotify_model['speechiness'])
viz_1['acousticness'] = np.mean(spotify_model['acousticness'])
viz_1['instrumentalness'] = np.mean(spotify_model['instrumentalness'])
viz_1['liveness'] = np.mean(spotify_model['liveness'])
viz_1['valence'] = np.mean(spotify_model['valence'])
viz_1['tempo'] = np.mean(spotify_model['tempo'])
viz_1['duration_ms'] = np.mean(spotify_model['duration_ms'])
viz_1['artist_n_tracks'] = np.mean(spotify_model['artist_n_tracks'])
viz_1['artist_hit_rate'] = np.mean(spotify_model['artist_hit_rate'])
viz_1['artist_energy_mean'] = np.mean(spotify_model['artist_energy_mean'])
viz_1['artist_danceability_mean'] = np.mean(spotify_model['artist_danceability_mean'])
viz_1['artist_valence_mean'] = np.mean(spotify_model['artist_valence_mean'])
viz_1['artist_tempo_mean'] = np.mean(spotify_model['artist_tempo_mean'])
viz_1['artist_acousticness_mean'] = np.mean(spotify_model['artist_acousticness_mean'])
viz_1['artist_speechiness_mean'] = np.mean(spotify_model['artist_speechiness_mean'])
viz_1['artist_instrumentalness_mean'] = np.mean(spotify_model['artist_instrumentalness_mean'])
viz_1['artist_liveness_mean'] = np.mean(spotify_model['artist_liveness_mean'])
viz_1['playlist_subgenre'] = spotify_model['playlist_subgenre'].mode()[0]
viz_1['mode'] = spotify_model['mode'].mode()[0]
viz_1['artist_n_genres'] = spotify_model['artist_n_genres'].mode()[0]
viz_1['key'] = spotify_model['key'].mode()[0]
viz_1.nunique()
artist_avg_popularity 101 playlist_avg_popularity 1 danceability 1 energy 1 speechiness 1 acousticness 1 instrumentalness 1 liveness 1 valence 1 tempo 1 duration_ms 1 artist_n_tracks 1 artist_hit_rate 1 artist_energy_mean 1 artist_danceability_mean 1 artist_valence_mean 1 artist_tempo_mean 1 artist_acousticness_mean 1 artist_speechiness_mean 1 artist_instrumentalness_mean 1 artist_liveness_mean 1 playlist_subgenre 1 mode 1 artist_n_genres 1 key 1 dtype: int64
m_4_pred_summary = m_4.get_prediction(viz_1).summary_frame()
m_4_pred_summary
| mean | mean_se | mean_ci_lower | mean_ci_upper | obs_ci_lower | obs_ci_upper | |
|---|---|---|---|---|---|---|
| 0 | -4.320376 | 0.668659 | -5.630980 | -3.009771 | -36.103661 | 27.462910 |
| 1 | -3.769062 | 0.664081 | -5.070692 | -2.467432 | -35.551979 | 28.013855 |
| 2 | -3.217748 | 0.659532 | -4.510463 | -1.925033 | -35.000301 | 28.564805 |
| 3 | -2.666434 | 0.655014 | -3.950293 | -1.382576 | -34.448628 | 29.115759 |
| 4 | -2.115121 | 0.650527 | -3.390184 | -0.840057 | -33.896960 | 29.666719 |
| ... | ... | ... | ... | ... | ... | ... |
| 96 | 48.605744 | 0.481134 | 47.662699 | 49.548789 | 16.835492 | 80.375996 |
| 97 | 49.157058 | 0.482888 | 48.210574 | 50.103541 | 17.386704 | 80.927412 |
| 98 | 49.708372 | 0.484719 | 48.758298 | 50.658445 | 17.937911 | 81.478833 |
| 99 | 50.259685 | 0.486628 | 49.305872 | 51.213499 | 18.489112 | 82.030258 |
| 100 | 50.810999 | 0.488611 | 49.853298 | 51.768700 | 19.040309 | 82.581689 |
101 rows × 6 columns
m_8_pred_summary = m_8.get_prediction(viz_1).summary_frame()
m_8_pred_summary
| mean | mean_se | mean_ci_lower | mean_ci_upper | obs_ci_lower | obs_ci_upper | |
|---|---|---|---|---|---|---|
| 0 | 6.900155 | 3.296670 | 0.438514 | 13.361797 | -22.237119 | 36.037430 |
| 1 | 7.045006 | 3.177685 | 0.816580 | 13.273432 | -22.041438 | 36.131450 |
| 2 | 7.159484 | 3.295956 | 0.699243 | 13.619725 | -21.977480 | 36.296448 |
| 3 | 7.247127 | 3.545053 | 0.298642 | 14.195611 | -22.001965 | 36.496219 |
| 4 | 7.311287 | 3.841407 | -0.218068 | 14.840641 | -22.081215 | 36.703788 |
| ... | ... | ... | ... | ... | ... | ... |
| 96 | 77.682430 | 4.547320 | 68.769451 | 86.595409 | 47.905440 | 107.459420 |
| 97 | 81.197296 | 5.314329 | 70.780940 | 91.613652 | 50.936291 | 111.458301 |
| 98 | 84.892864 | 6.209965 | 72.721015 | 97.064713 | 53.983612 | 115.802116 |
| 99 | 88.777785 | 7.241089 | 74.584880 | 102.970690 | 57.018274 | 120.537295 |
| 100 | 92.861005 | 8.415416 | 76.366361 | 109.355649 | 60.008285 | 125.713726 |
101 rows × 6 columns
fig, ax = plt.subplots()
ax.fill_between(dfA_viz_b.x2,
fit_A_pred_summary_b.obs_ci_lower, fit_A_pred_summary_b.obs_ci_upper,
facecolor='orange', alpha=0.75, edgecolor='orange')
ax.fill_between(dfA_viz_b.x2,
fit_A_pred_summary_b.mean_ci_lower, fit_A_pred_summary_b.mean_ci_upper,
facecolor='grey',edgecolor='grey')
ax.plot(dfA_viz_b.x2, fit_A_pred_summary_b['mean'], color='k',linewidth=1)
ax.set_xlabel('x2')
ax.set_ylabel('y')
plt.show()
# Create visualization for both models
fig, axes = plt.subplots(1, 2, figsize=(15, 6))
# Model 4 (All inputs additive) - Left plot
ax1 = axes[0]
ax1.fill_between(viz_1['artist_avg_popularity'],
m_4_pred_summary['obs_ci_lower'], m_4_pred_summary['obs_ci_upper'],
facecolor='orange', alpha=0.75, edgecolor='orange', label='Prediction Interval (95%)')
ax1.fill_between(viz_1['artist_avg_popularity'],
m_4_pred_summary['mean_ci_lower'], m_4_pred_summary['mean_ci_upper'],
facecolor='grey', edgecolor='grey', alpha=0.6, label='Confidence Interval (95%)')
ax1.plot(viz_1['artist_avg_popularity'], m_4_pred_summary['mean'], color='k', linewidth=2, label='Mean Prediction')
ax1.set_xlabel('Artist Average Popularity')
ax1.set_ylabel('Predicted Track Popularity')
ax1.set_title('Model 4: All Inputs Additive')
ax1.legend()
ax1.grid(True, alpha=0.3)
# Model 6 (Artist-Category Interactions) - Right plot
ax2 = axes[1]
ax2.fill_between(viz_1['artist_avg_popularity'],
m_8_pred_summary['obs_ci_lower'], m_8_pred_summary['obs_ci_upper'],
facecolor='orange', alpha=0.75, edgecolor='orange', label='Prediction Interval (95%)')
ax2.fill_between(viz_1['artist_avg_popularity'],
m_8_pred_summary['mean_ci_lower'], m_8_pred_summary['mean_ci_upper'],
facecolor='grey', edgecolor='grey', alpha=0.6, label='Confidence Interval (95%)')
ax2.plot(viz_1['artist_avg_popularity'], m_8_pred_summary['mean'], color='k', linewidth=2, label='Mean Prediction')
ax2.set_xlabel('Artist Average Popularity')
ax2.set_ylabel('Predicted Track Popularity')
ax2.set_title('Model 8: Complex Polynomial Interactions')
ax2.legend()
ax2.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
Model 4 is essentially staight line with tighter confidence interval. In constrast, model 7 displays polynomial shape with curvature and more exapnded intervals. Significantly, model 8 does not predict negative track popularity unlike model 4.
You must identify the THREE most important inputs based on the statistically significant coefficients in your models. One of the three must be the SAME input you selected for grid 1. This input will have 101 unique values in the grid 2, just as it did in grid 1. The two other inputs must have fewer unique values in the grid. Categorical inputs should use all unique values (categories). Continuous inputs should use 5 unique values between the training set minimum and maximum values.
viz_2 = pd.DataFrame([
(x1, x2, x3)
for x1 in np.linspace(np.min(spotify_model['artist_avg_popularity']),
np.max(spotify_model['artist_avg_popularity']), num=101)
for x2 in spotify_model['playlist_subgenre'].unique()
for x3 in np.linspace(np.min(spotify_model['playlist_avg_popularity']),
np.max(spotify_model['playlist_avg_popularity']), num=5)
], columns=['artist_avg_popularity', 'playlist_subgenre', 'playlist_avg_popularity'])
viz_2 = pd.DataFrame([
(x1, x2, x3)
for x1 in np.linspace(np.min(spotify_model['artist_avg_popularity']),
np.max(spotify_model['artist_avg_popularity']), num=101)
for x2 in np.linspace(np.min(spotify_model['artist_hit_rate']),
np.max(spotify_model['artist_hit_rate']), num=5)
for x3 in np.linspace(np.min(spotify_model['playlist_avg_popularity']),
np.max(spotify_model['playlist_avg_popularity']), num=5)
], columns=['artist_avg_popularity', 'artist_hit_rate', 'playlist_avg_popularity'])
viz_2['artist_hit_rate'] = np.mean(spotify_model['artist_hit_rate'])
viz_2['danceability'] = np.mean(spotify_model['danceability'])
viz_2['energy'] = np.mean(spotify_model['energy'])
viz_2['speechiness'] = np.mean(spotify_model['speechiness'])
viz_2['acousticness'] = np.mean(spotify_model['acousticness'])
viz_2['instrumentalness'] = np.mean(spotify_model['instrumentalness'])
viz_2['liveness'] = np.mean(spotify_model['liveness'])
viz_2['valence'] = np.mean(spotify_model['valence'])
viz_2['tempo'] = np.mean(spotify_model['tempo'])
viz_2['duration_ms'] = np.mean(spotify_model['duration_ms'])
viz_2['artist_n_tracks'] = np.mean(spotify_model['artist_n_tracks'])
viz_2['artist_energy_mean'] = np.mean(spotify_model['artist_energy_mean'])
viz_2['artist_danceability_mean'] = np.mean(spotify_model['artist_danceability_mean'])
viz_2['artist_valence_mean'] = np.mean(spotify_model['artist_valence_mean'])
viz_2['artist_tempo_mean'] = np.mean(spotify_model['artist_tempo_mean'])
viz_2['artist_acousticness_mean'] = np.mean(spotify_model['artist_acousticness_mean'])
viz_2['artist_speechiness_mean'] = np.mean(spotify_model['artist_speechiness_mean'])
viz_2['artist_instrumentalness_mean'] = np.mean(spotify_model['artist_instrumentalness_mean'])
viz_2['artist_liveness_mean'] = np.mean(spotify_model['artist_liveness_mean'])
viz_2['mode'] = spotify_model['mode'].mode()[0]
viz_2['artist_n_genres'] = spotify_model['artist_n_genres'].mode()[0]
viz_2['key'] = spotify_model['key'].mode()[0]
viz_2['playlist_subgenre'] = spotify_model['playlist_subgenre'].mode()[0]
viz_2['mode'] = spotify_model['mode'].mode()[0]
viz_2['artist_n_genres'] = spotify_model['artist_n_genres'].mode()[0]
viz_2['key'] = spotify_model['key'].mode()[0]
viz_2.nunique()
artist_avg_popularity 101 playlist_subgenre 24 playlist_avg_popularity 5 artist_hit_rate 1 danceability 1 energy 1 speechiness 1 acousticness 1 instrumentalness 1 liveness 1 valence 1 tempo 1 duration_ms 1 artist_n_tracks 1 artist_energy_mean 1 artist_danceability_mean 1 artist_valence_mean 1 artist_tempo_mean 1 artist_acousticness_mean 1 artist_speechiness_mean 1 artist_instrumentalness_mean 1 artist_liveness_mean 1 mode 1 artist_n_genres 1 key 1 dtype: int64
Make predictions with BOTH models on the visualization grid. You MUST visualize the AVERAGE OUTPUT as a line with respect to the input with the 101 unique values in the visualization grid. The line must be colored by one of the two other inputs with non-constant values. The third input must be associated with the facets. It is your choice as to which input is associated with the line color (hue) versus the facets. If you color by a continuous variable, you should use a diverging color palette. You may use the default color palette for coloring by a categorical variable.
m_4_pred_summary_2 = m_4.get_prediction(viz_2).summary_frame()
m_8_pred_summary_2 = m_8.get_prediction(viz_2).summary_frame()
dfviz2 = pd.DataFrame({
'artist_avg_popularity': viz_2['artist_avg_popularity'],
'm4_pred': m_4_pred_summary_2['mean'],
'm8_pred': m_8_pred_summary_2['mean'],
'playlist_subgenre': viz_2['playlist_subgenre'],
'playlist_avg_popularity': viz_2['playlist_avg_popularity']
})
sns.relplot(data=dfviz2, x='artist_avg_popularity', y='m4_pred', hue='playlist_avg_popularity',
kind='line', aspect=1.5, col='playlist_subgenre', col_wrap=4,
facet_kws={'sharey': False})
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
sns.relplot(data=dfviz2,x='artist_avg_popularity',y='m8_pred',row='playlist_subgenre',kind='line',aspect=1.5,col='playlist_avg_popularity', facet_kws={'sharey': False})
plt.show()
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight self._figure.tight_layout(*args, **kwargs)
The predictions by the two models indciate several things. Model 4 indicates consistent predictions for unseen data. It also shows associates
The more complex model, model 8, on the other hand, contain non linear interactions as indicated by the curved graphs. This is natural as it was constructed with many embedded interactions. However, the model predicts extremely negative values for several subgenres. This indicates potential overfit.
This is not seen with model 4 however. We see more consistent values that are more reasonable. There are some subgenres where track popularity drops below 0 but it is consistent for the most part. This indicates that model 4 will perform better on unforseen data while model 8 already performs much worst.
Models: Performance and Validation¶
You must select the formulation that was the best model on the training set.
The best formulation was Polynomial Interaction model 7.
You must choose 2 additional formulations. One should be simple (few features), and one should be of medium to high complexity.
Simple model would be continuous only inputs. model 3
Medium complexity is model 5 that has interaction terms between continuous and categoricals.
You must use CROSS-VALIDATION to evaluate the performance for each of the 3 models. Using “regular” K-fold OR stratified K-fold depends on whether you are working on a REGRESSION or CLASSIFICATION problem. You may choose 5-fold, 10-fold, or repeated cross-validation. You must identify an appropriate performance metric to focus on based on the output data type.
from sklearn.linear_model import LinearRegression
from patsy import dmatrices
def fit_and_assess_linearregression(mod_name, a_formula, the_data):
# create arrays
y, X = dmatrices(a_formula, data=the_data)
a_mod = LinearRegression(fit_intercept=False).fit( X, y.ravel() )
res_dict = {'model_name': mod_name,
'model_formula': a_formula,
'num_coefs': a_mod.coef_.size,
'R-squared': a_mod.score(X, y.ravel())}
return pd.DataFrame( res_dict, index=[0] )
linearregression_results_list = []
models = [1,2,3,4,5,6,7,8]
for m in models:
linearregression_results_list.append(
fit_and_assess_linearregression(f'Model {m}', eval(f'f_{m}'), spotify_model)
)
linearregression_results_df = pd.concat(linearregression_results_list, ignore_index=True)
linearregression_results_df
| model_name | model_formula | num_coefs | R-squared | |
|---|---|---|---|---|
| 0 | Model 1 | track_popularity ~ 1 | 1 | 0.000000 |
| 1 | Model 2 | track_popularity ~ +playlist_subgenre + mode ... | 27 | 0.154829 |
| 2 | Model 3 | track_popularity ~ danceability + energy + sp... | 22 | 0.527651 |
| 3 | Model 4 | track_popularity ~ danceability + energy + sp... | 48 | 0.533418 |
| 4 | Model 5 | track_popularity ~ (danceability + energy + s... | 92 | 0.581912 |
| 5 | Model 6 | track_popularity ~ artist_avg_popularity*(danc... | 104 | 0.585522 |
| 6 | Model 7 | track_popularity ~ (artist_avg_popularity + ... | 456 | 0.623967 |
| 7 | Model 8 | track_popularity ~ (I(artist_avg_popularity*... | 780 | 0.647324 |
from sklearn.model_selection import KFold
kf = KFold(n_splits=5, shuffle=True, random_state=101)
from sklearn.model_selection import cross_val_score
def lm_cross_val_score(mod_name, a_formula, init_mod, the_data, cv):
# create the feature and output arrays using the formula
y, X = dmatrices( a_formula+"-1", data=the_data )
# train and test within each fold - return the test set scores
# rsquared
test_r2 = cross_val_score( init_mod, X, y.ravel(), cv=cv )
# rmse
test_rmse = -cross_val_score( init_mod, X, y.ravel(), cv=cv, scoring='neg_root_mean_squared_error' )
# book keeping
res_df=pd.DataFrame({'R-squared': test_r2,
'RMSE': test_rmse})
res_df['fold_id'] = res_df.index + 1
res_df['model_name'] = mod_name
res_df['model_formula'] = a_formula
res_df['num_coefs'] = X.shape[1]
return res_df
We retrieve the data before there was any standardization
spotify_model = spotify.copy()
spotify_model = spotify_model.merge(artist_vars, on='track_artist', how='inner')
spotify_model = spotify_model.merge(playlist_vars, on='playlist_id', how='inner')
cont_var = ['danceability', 'energy','speechiness',
'acousticness', 'instrumentalness', 'liveness', 'valence',
'tempo', 'duration_ms', 'artist_avg_popularity',
'artist_n_tracks',
'artist_hit_rate',
'artist_energy_mean',
'artist_danceability_mean',
'artist_valence_mean',
'artist_tempo_mean',
'artist_acousticness_mean',
'artist_speechiness_mean',
'artist_instrumentalness_mean',
'artist_liveness_mean','playlist_avg_popularity']
cat_var = ['playlist_subgenre', 'mode','artist_n_genres', 'key']
spotify_model[cat_var] = spotify_model[cat_var].astype('category')
spotify_model[cont_var] = np.log1p(spotify_model[cont_var])
from sklearn.pipeline import Pipeline
lm = LinearRegression()
# Define the pipeline correctly
lm = LinearRegression()
model_flow = Pipeline([('standardize', StandardScaler()), ('fit', lm)])
# Test it with actual data
y, X = dmatrices(f_4+"-1", data=spotify_model) # Use an actual formula
z = model_flow.fit(X, y.ravel())
print(f"Pipeline R-squared: {z.score(X, y.ravel())}")
Pipeline R-squared: 0.5339279812076785
model_flow = Pipeline( steps=[ ('standardize', StandardScaler()),('fit', lm) ] )
cv_score_list = []
models = [1,2,3,4,5,6,7,8]
for m in models:
cv_score_list.append(
lm_cross_val_score(f'Model {m}', eval(f'f_{m}'), model_flow, spotify_model, kf)
)
cv_score_df = pd.concat(cv_score_list, ignore_index=True)
sns.catplot(data = cv_score_df, x='model_name', y='R-squared', kind='point', aspect=1.5, join=False,errorbar=('ci',95))
plt.show()
C:\Users\pc\AppData\Local\Temp\ipykernel_15864\2824232948.py:1: UserWarning:
The `join` parameter is deprecated and will be removed in v0.15.0. You can remove the line between points with `linestyle='none'`.
sns.catplot(data = cv_score_df, x='model_name', y='R-squared', kind='point', aspect=1.5, join=False,errorbar=('ci',95))
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
sns.catplot(data = cv_score_df, x='model_name', y='RMSE', kind='point', aspect=1.5, join=False,errorbar=('ci',95))
plt.show()
C:\Users\pc\AppData\Local\Temp\ipykernel_15864\632921638.py:1: UserWarning:
The `join` parameter is deprecated and will be removed in v0.15.0. You can remove the line between points with `linestyle='none'`.
sns.catplot(data = cv_score_df, x='model_name', y='RMSE', kind='point', aspect=1.5, join=False,errorbar=('ci',95))
d:\Anaconda\venv\cmpin2100\lib\site-packages\seaborn\axisgrid.py:123: UserWarning: The figure layout has changed to tight
self._figure.tight_layout(*args, **kwargs)
Which model is the BEST according to CROSS-VALIDATION?
cv_score_df
| R-squared | RMSE | fold_id | model_name | model_formula | num_coefs | |
|---|---|---|---|---|---|---|
| 0 | -0.000662 | 23.637349 | 1 | Model 1 | track_popularity ~ 1 | 1 |
| 1 | -0.000082 | 23.359256 | 2 | Model 1 | track_popularity ~ 1 | 1 |
| 2 | -0.000968 | 24.082243 | 3 | Model 1 | track_popularity ~ 1 | 1 |
| 3 | -0.000061 | 23.640301 | 4 | Model 1 | track_popularity ~ 1 | 1 |
| 4 | -0.000023 | 23.777993 | 5 | Model 1 | track_popularity ~ 1 | 1 |
| 5 | 0.152738 | 21.750227 | 1 | Model 2 | track_popularity ~ +playlist_subgenre + mode ... | 40 |
| 6 | 0.159812 | 21.410636 | 2 | Model 2 | track_popularity ~ +playlist_subgenre + mode ... | 40 |
| 7 | 0.151861 | 22.167685 | 3 | Model 2 | track_popularity ~ +playlist_subgenre + mode ... | 40 |
| 8 | 0.158546 | 21.684781 | 4 | Model 2 | track_popularity ~ +playlist_subgenre + mode ... | 40 |
| 9 | 0.157595 | 21.823817 | 5 | Model 2 | track_popularity ~ +playlist_subgenre + mode ... | 40 |
| 10 | 0.519846 | 16.373648 | 1 | Model 3 | track_popularity ~ danceability + energy + sp... | 22 |
| 11 | 0.529176 | 16.027670 | 2 | Model 3 | track_popularity ~ danceability + energy + sp... | 22 |
| 12 | 0.532567 | 16.456841 | 3 | Model 3 | track_popularity ~ danceability + energy + sp... | 22 |
| 13 | 0.529141 | 16.221290 | 4 | Model 3 | track_popularity ~ danceability + energy + sp... | 22 |
| 14 | 0.523366 | 16.415829 | 5 | Model 3 | track_popularity ~ danceability + energy + sp... | 22 |
| 15 | 0.523710 | 16.307626 | 1 | Model 4 | track_popularity ~ danceability + energy + sp... | 61 |
| 16 | 0.534520 | 15.936459 | 2 | Model 4 | track_popularity ~ danceability + energy + sp... | 61 |
| 17 | 0.537150 | 16.375966 | 3 | Model 4 | track_popularity ~ danceability + energy + sp... | 61 |
| 18 | 0.533729 | 16.142057 | 4 | Model 4 | track_popularity ~ danceability + energy + sp... | 61 |
| 19 | 0.528999 | 16.318539 | 5 | Model 4 | track_popularity ~ danceability + energy + sp... | 61 |
| 20 | 0.568206 | 15.527209 | 1 | Model 5 | track_popularity ~ (danceability + energy + s... | 92 |
| 21 | 0.581225 | 15.115820 | 2 | Model 5 | track_popularity ~ (danceability + energy + s... | 92 |
| 22 | 0.587461 | 15.460344 | 3 | Model 5 | track_popularity ~ (danceability + energy + s... | 92 |
| 23 | 0.584941 | 15.229818 | 4 | Model 5 | track_popularity ~ (danceability + energy + s... | 92 |
| 24 | 0.570745 | 15.578579 | 5 | Model 5 | track_popularity ~ (danceability + energy + s... | 92 |
| 25 | 0.571844 | 15.461661 | 1 | Model 6 | track_popularity ~ artist_avg_popularity*(danc... | 143 |
| 26 | 0.583971 | 15.066168 | 2 | Model 6 | track_popularity ~ artist_avg_popularity*(danc... | 143 |
| 27 | 0.590122 | 15.410406 | 3 | Model 6 | track_popularity ~ artist_avg_popularity*(danc... | 143 |
| 28 | 0.590970 | 15.118800 | 4 | Model 6 | track_popularity ~ artist_avg_popularity*(danc... | 143 |
| 29 | 0.576505 | 15.473702 | 5 | Model 6 | track_popularity ~ artist_avg_popularity*(danc... | 143 |
| 30 | 0.597202 | 14.996806 | 1 | Model 7 | track_popularity ~ (artist_avg_popularity + ... | 456 |
| 31 | 0.611079 | 14.567059 | 2 | Model 7 | track_popularity ~ (artist_avg_popularity + ... | 456 |
| 32 | 0.618149 | 14.874204 | 3 | Model 7 | track_popularity ~ (artist_avg_popularity + ... | 456 |
| 33 | 0.607380 | 14.812420 | 4 | Model 7 | track_popularity ~ (artist_avg_popularity + ... | 456 |
| 34 | 0.605557 | 14.933517 | 5 | Model 7 | track_popularity ~ (artist_avg_popularity + ... | 456 |
| 35 | 0.577814 | 15.353484 | 1 | Model 8 | track_popularity ~ (artist_avg_popularity + ... | 1320 |
| 36 | 0.343735 | 18.922597 | 2 | Model 8 | track_popularity ~ (artist_avg_popularity + ... | 1320 |
| 37 | 0.469790 | 17.527131 | 3 | Model 8 | track_popularity ~ (artist_avg_popularity + ... | 1320 |
| 38 | -92365.606117 | 7184.512656 | 4 | Model 8 | track_popularity ~ (artist_avg_popularity + ... | 1320 |
| 39 | 0.596897 | 15.096571 | 5 | Model 8 | track_popularity ~ (artist_avg_popularity + ... | 1320 |
print(cv_score_df.groupby('model_name')['RMSE'].mean().reset_index().sort_values('RMSE').iloc[0])
model_name Model 7 RMSE 14.836801 Name: 6, dtype: object
Model 7 has the lowest RMSE and therefore highest R squared. Therefore, it is the best model.
Is this model DIFFERENT from the model identified as the BEST according to the training set?
Yes. Training perforamnce indicated model 7 to be the best.
linearregression_results_df.groupby('model_name')['R-squared'].max().reset_index().sort_values('R-squared', ascending=False).iloc[0].values == cv_score_df.groupby('model_name')['R-squared'].mean().reset_index().sort_values('R-squared').iloc[0]
model_name True R-squared False Name: 7, dtype: bool
No it was not. Training performance favored the most complex model. In cross validation, the most complext model performed the worst than intercept only model.
How many regression coefficients are associated with the best model?
cv_score_df.groupby(['model_name','num_coefs'])['RMSE'].mean().reset_index().sort_values('RMSE').iloc[0]
model_name Model 7 num_coefs 456 RMSE 14.836801 Name: 6, dtype: object
There were 456 coefficients.